Author Topic: Implicit differentiation?? (Read 1112 times) Tweet Share

superflya · « **on:** December 30, 2009, 07:36:07 pm »

can anyone explain it in simple terms, the examples in the essentials book arent too much help :S

thanks

GerrySly · « **Reply #1 on:** December 30, 2009, 07:48:57 pm »

It's just the chain rule basically, for example let's take the equation $x^2+y^2=4$

$\begin{align*} \frac{d}{dx}(4)&=\frac{d}{dx}(x^2)+\frac{d}{dx}(y^2)\\ 0&=2x+\frac{dy}{dx}\frac{d}{dy}(y^2)\\ &=2x+2y\frac{dy}{dx}\\ -2y\frac{dy}{dx}&=2x\\ \frac{dy}{dx}&=-\frac{x}{y} \end{align*}$

So you just differentiate $d^2$ with respect to x, but $y^2$ can't be done that easily, so to do it you basically apply the chain rule to $\frac{d}{dx}&=\frac{d}{}\frac{}{dx}&=\frac{d}{dy}\frac{dy}{dx}$ . Then you work out $\frac{d}{dy}(y^2)$ and rearrange for $\frac{dy}{dx}$

superflya · « **Reply #2 on:** December 30, 2009, 07:56:00 pm »

thanks a mill, makes heaps more sense

kyzoo · « **Reply #3 on:** December 30, 2009, 10:30:58 pm »

I see it as just differentiating the whole equation. It's just like multiplying both sides of an equation by a constant, or "powering" both sides.

superflya · « **Reply #4 on:** December 30, 2009, 10:48:29 pm »

yea ive got it now, completed the exercise pretty straight forward

Search the forums now!

We have moved!

Author Topic: Implicit differentiation?? (Read 1112 times) Tweet Share

superflya

Implicit differentiation??

GerrySly

Re: Implicit differentiation??

superflya

Re: Implicit differentiation??

kyzoo

Re: Implicit differentiation??

superflya

Re: Implicit differentiation??

Recent Posts

User:
Password: