Question

Help with implicit differentiation? :)

Answer 1

Of?

Answer 2

Well, I need to head out and it looks like the site is going slow. If you are able to read this, here is a great reference for calculus:
http://tutorial.math.lamar.edu/Classes/CalcI/ImplicitDIff.aspx

That might get you through implicit.

Answer 3

@e.mccormick -- Apologies; I was wondering if I was the only one having issues with the site; guess not. I'll be sure to look at it, though. I'll post the problem I'm having issues with, though.

Answer 4

The problem is: Use Implicit Differentiation and the Product Rule to determine: \[\frac{ dy }{ dx } [x*\sin(y)=3]\]

Answer 5

Differentiate each term
For xsin(y), use product rule,
For 3, if you differentiate a constant is zero
\[xcos(y)\frac{dy}{dx}+\sin(y)(1)=0 \\ \\ \frac{dy}{dx}=-\frac{ysin(y)}{\cos(y)} \\ \\ \frac{dy}{dx}=-ytan(y)\]

Answer 6

No need to apologize for having trouble with a site that is more than a little buggy!

.Sam. walked through the problem, so no need for me to go into that particular one, but I thought I would add a general note that I hope helps.

Remember in regular differentiation how you use the chain rule? \(f(g(x))\) differentiates to \(f'(g(x))g'(x)\). Implicit is the same basic concept. You get something representing the function as a whole and it is multiplied by something representing the derivative of it.

So whenever you hit y, you get y and y' multiplying it. But because y is in terms of x, y' becomes \(\frac{dy}{dx}\).

That is the whole big secret. It is the same basic thing you have done before. And you have done it tons of times in different ways. Like \(\frac{dy}{dx}e^{4x^2}=8xe^{4x^2}\) That works very much the same way as the whole implicit part of calculus.

So why do people find implicit hard? It is not the calculus! It is the algebra and trig. Usually implicit differentiation ends up making a long and messy answer that needs to be simplified. That is where the mistakes are usually made.

I hope that helps some by giving you something you know to associate with implicit and exposes the dirty little secret about calculus. The calculus part is usually not too bad. It is the rest of it that gets you!