A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

aufheben1
 one year ago
Best ResponseYou've already chosen the best response.1short answer: take the equation: y = sin(3x +4y). how can we take the derivative here? the x and y terms are 'mixed in' together. implicit differentiation is a technique to take the derivative here without having to change the equation around first. this may be confusing, so the longer answer below clarifies! first, let's consider ''regular'' differentiation. we have some function y=f(x) where y is alone on the left and there are only x terms on the right. we calculate dy/dx (also known as f'(x)) using all the tools we've learnedproduct rule, chain rule, etc. notice that y is written alone on one side and the 'function' written out on the other. this is called writing a function "explicitly" because y is shown "explicitly" (clearly) to be equal to the function written out on the other side. now, consider instead a more complicated equation where y and x terms are mixed up and appear on both sides of the equation! for example, the equation of a circle is often written this way: \[x ^{2} + y ^{2} = r ^{2}\]notice that the value of y is not written out explicitly or clearly. to know exactly what y is in terms of x, we would have to solve for y. this would be ONE way to take the derivative of the function: solve for y and then to take the derivative as we normally would. HOWEVER, there are two drawbacks to this method. first  we have to solve for y before we even get started with our real goal, taking the derivative. second  sometimes we want the derivatives of equations which are really hard to solve for yeven impossible! in this case, it would be better to be able to take the derivative without having to solve for y first. AHA! this is what implicit differentiation is: taking the derivative of a or relation when y is not already alone on one side of the equation. for example: y=sin(3x +4y). HOW would you take the derivative? solving for y? NO WAY! we want a technique to take the derivative of this function AS IT IS WRITTEN. that technique is called implicit differentiation.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.