Understanding operator under a subtitution












3














in my notes, I have the following phrase:



With $x = e^t$ and $x frac{d}{dx} = frac{d}{dt}$



How, how come we get $x frac{d}{dx} = frac{d}{dt} $? I know if I diferentiate with respect to $t$ I obtain



$$ frac{d}{dt} x = x $$



I do not understand how this operators are defined? maybe I am misunderstading the notation?






calculus







share|cite|improve this question



























    3














    in my notes, I have the following phrase:



    With $x = e^t$ and $x frac{d}{dx} = frac{d}{dt}$



    How, how come we get $x frac{d}{dx} = frac{d}{dt} $? I know if I diferentiate with respect to $t$ I obtain



    $$ frac{d}{dt} x = x $$



    I do not understand how this operators are defined? maybe I am misunderstading the notation?






    calculus







    share|cite|improve this question

























      3












      3








      3


      1





      in my notes, I have the following phrase:



      With $x = e^t$ and $x frac{d}{dx} = frac{d}{dt}$



      How, how come we get $x frac{d}{dx} = frac{d}{dt} $? I know if I diferentiate with respect to $t$ I obtain



      $$ frac{d}{dt} x = x $$



      I do not understand how this operators are defined? maybe I am misunderstading the notation?






      calculus







      share|cite|improve this question













      in my notes, I have the following phrase:



      With $x = e^t$ and $x frac{d}{dx} = frac{d}{dt}$



      How, how come we get $x frac{d}{dx} = frac{d}{dt} $? I know if I diferentiate with respect to $t$ I obtain



      $$ frac{d}{dt} x = x $$



      I do not understand how this operators are defined? maybe I am misunderstading the notation?






      calculus




      calculus






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 2 hours ago









      Jimmy SabaterJimmy Sabater

      1,997219




      1,997219






















          2 Answers
          2






          active

          oldest

          votes


















          2














          With



          $x = e^t tag 1$



          we have



          $dfrac{dx}{dt} = e^t = x; tag 2$



          thus for any function $f$



          $xdfrac{df}{dx} = dfrac{dx}{dt} dfrac{df}{dx} = dfrac{df}{dt} tag 3$



          by the chain rule. Thus,



          $xdfrac{d}{dx} = dfrac{d}{dt}. tag 4$






          share|cite|improve this answer





























            2














            $frac {dy} {dt} =frac {dy} {dx}frac {dx} {dt} =frac {dy} {dx} e^{t}=frac {dy} {dx} x$.






            share|cite|improve this answer





















              Your Answer





              StackExchange.ifUsing("editor", function () {
              return StackExchange.using("mathjaxEditing", function () {
              StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
              StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
              });
              });
              }, "mathjax-editing");

              StackExchange.ready(function() {
              var channelOptions = {
              tags: "".split(" "),
              id: "69"
              };
              initTagRenderer("".split(" "), "".split(" "), channelOptions);

              StackExchange.using("externalEditor", function() {
              // Have to fire editor after snippets, if snippets enabled
              if (StackExchange.settings.snippets.snippetsEnabled) {
              StackExchange.using("snippets", function() {
              createEditor();
              });
              }
              else {
              createEditor();
              }
              });

              function createEditor() {
              StackExchange.prepareEditor({
              heartbeatType: 'answer',
              autoActivateHeartbeat: false,
              convertImagesToLinks: true,
              noModals: true,
              showLowRepImageUploadWarning: true,
              reputationToPostImages: 10,
              bindNavPrevention: true,
              postfix: "",
              imageUploader: {
              brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
              contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
              allowUrls: true
              },
              noCode: true, onDemand: true,
              discardSelector: ".discard-answer"
              ,immediatelyShowMarkdownHelp:true
              });


              }
              });














              draft saved

              draft discarded


















              StackExchange.ready(
              function () {
              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3067102%2funderstanding-operator-under-a-subtitution%23new-answer', 'question_page');
              }
              );

              Post as a guest















              Required, but never shown

























              2 Answers
              2






              active

              oldest

              votes








              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              2














              With



              $x = e^t tag 1$



              we have



              $dfrac{dx}{dt} = e^t = x; tag 2$



              thus for any function $f$



              $xdfrac{df}{dx} = dfrac{dx}{dt} dfrac{df}{dx} = dfrac{df}{dt} tag 3$



              by the chain rule. Thus,



              $xdfrac{d}{dx} = dfrac{d}{dt}. tag 4$






              share|cite|improve this answer


























                2














                With



                $x = e^t tag 1$



                we have



                $dfrac{dx}{dt} = e^t = x; tag 2$



                thus for any function $f$



                $xdfrac{df}{dx} = dfrac{dx}{dt} dfrac{df}{dx} = dfrac{df}{dt} tag 3$



                by the chain rule. Thus,



                $xdfrac{d}{dx} = dfrac{d}{dt}. tag 4$






                share|cite|improve this answer
























                  2












                  2








                  2






                  With



                  $x = e^t tag 1$



                  we have



                  $dfrac{dx}{dt} = e^t = x; tag 2$



                  thus for any function $f$



                  $xdfrac{df}{dx} = dfrac{dx}{dt} dfrac{df}{dx} = dfrac{df}{dt} tag 3$



                  by the chain rule. Thus,



                  $xdfrac{d}{dx} = dfrac{d}{dt}. tag 4$






                  share|cite|improve this answer












                  With



                  $x = e^t tag 1$



                  we have



                  $dfrac{dx}{dt} = e^t = x; tag 2$



                  thus for any function $f$



                  $xdfrac{df}{dx} = dfrac{dx}{dt} dfrac{df}{dx} = dfrac{df}{dt} tag 3$



                  by the chain rule. Thus,



                  $xdfrac{d}{dx} = dfrac{d}{dt}. tag 4$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 2 hours ago









                  Robert LewisRobert Lewis

                  44k22963




                  44k22963























                      2














                      $frac {dy} {dt} =frac {dy} {dx}frac {dx} {dt} =frac {dy} {dx} e^{t}=frac {dy} {dx} x$.






                      share|cite|improve this answer


























                        2














                        $frac {dy} {dt} =frac {dy} {dx}frac {dx} {dt} =frac {dy} {dx} e^{t}=frac {dy} {dx} x$.






                        share|cite|improve this answer
























                          2












                          2








                          2






                          $frac {dy} {dt} =frac {dy} {dx}frac {dx} {dt} =frac {dy} {dx} e^{t}=frac {dy} {dx} x$.






                          share|cite|improve this answer












                          $frac {dy} {dt} =frac {dy} {dx}frac {dx} {dt} =frac {dy} {dx} e^{t}=frac {dy} {dx} x$.







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered 2 hours ago









                          Kavi Rama MurthyKavi Rama Murthy

                          51.8k32055




                          51.8k32055






























                              draft saved

                              draft discarded




















































                              Thanks for contributing an answer to Mathematics Stack Exchange!


                              • Please be sure to answer the question. Provide details and share your research!

                              But avoid …



                              • Asking for help, clarification, or responding to other answers.

                              • Making statements based on opinion; back them up with references or personal experience.


                              Use MathJax to format equations. MathJax reference.


                              To learn more, see our tips on writing great answers.





                              Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                              Please pay close attention to the following guidance:


                              • Please be sure to answer the question. Provide details and share your research!

                              But avoid …



                              • Asking for help, clarification, or responding to other answers.

                              • Making statements based on opinion; back them up with references or personal experience.


                              To learn more, see our tips on writing great answers.




                              draft saved


                              draft discarded














                              StackExchange.ready(
                              function () {
                              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3067102%2funderstanding-operator-under-a-subtitution%23new-answer', 'question_page');
                              }
                              );

                              Post as a guest















                              Required, but never shown





















































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown

































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown







                              -

                              Popular posts from this blog

                              404 Error Contact Form 7 ajax form submitting

                              Image
                              0 The contact form does not work, and affects loading after one try. The chrome console shows the error message: POST http://example.com/wp-json/contact-form-7/v1/contact-forms/50/feedback 404 (Not Found) send @ jquery.js?ver=1.12.4:4 ajax @ jquery.js?ver=1.12.4:4 wpcf7.submit @ scripts.js?ver=5.0.3:346 (anonymous) @ scripts.js?ver=5.0.3:53 dispatch @ jquery.js?ver=1.12.4:3 r.handle @ jquery.js?ver=1.12.4:3 How to solve this issue? thanks in advance javascript wordpress contact-form-7 share | improve this question edited Jul 17 '18 at 5:39 Kiran Shahi 4,745 3 16 43 ...
                              Read more

                              How to know if a Active Directory user can login interactively

                              Image
                              1 I would like to know if and how is it possible to know if a AD user can login interactively (on a server) in a domain. I need to know if I can find it out using a LDAP search. Thanks. windows active-directory login user-permissions user-profile share | improve this question edited 1 hour ago yagmoth555 ♦ 11.6k 3 17 42 asked 1 hour ago Luigi Luigi 6 1 New contributor ...
                              Read more

                              Refactoring coordinates for Minecraft Pi buildings written in Python

                              Image
                              0 $begingroup$ I'm fairly new to coding and I wrote this script in Python for a house with a roof in Minecraft Pi. I've found different ways to write the coordinates to make the code base shorter, but I'm wondering if it is possible for me to refactor it any further so I don't have to list each coordinate line by line. import mcpi.minecraft as minecraft import mcpi.block as block mc = minecraft.Minecraft.create() p = mc.player.getTilePos() mc.setBlocks(p.x+1, p.y, p.z+1, #Main structure starting coordinates (DO NOT ALTER) p.x+19, p.y+4, p.z+6, #Structure size/coordinates (Alters cube size) block.STONE_BRICK) mc.setBlocks(p.x+2, p.y+1, p.z+2, #Hollowing out main structure interior p.x+18, p.y+3, p.z+5, block.AIR) mc.setBlocks(p.x, p.y...
                              Read more