# Thread: Implicit Differentiation

1. ## Implicit Differentiation

Im trying to find tangency points in a problem so I need to differentiate, $x^2+y^2=4000^2$

Why is the derivative of y2=0? I thought by the laws of implicit differentiation that you just multiply the y term by its derivative which then follows the same rules as x does, so using the power rule would result with y2=2y. Why does y2=0 then when I plugin the formula into wolfram?

2. ## Re: Implicit Differentiation

Originally Posted by Greymalkin
Im trying to find tangency points in a problem so I need to differentiate, $x^2+y^2=4000^2$
The derivative is $y'=\frac{-x}{y}~.$

3. ## Re: Implicit Differentiation

Originally Posted by Greymalkin
Im trying to find tangency points in a problem so I need to differentiate, $x^2+y^2=4000^2$

Why is the derivative of y2=0? I thought by the laws of implicit differentiation that you just multiply the y term by its derivative which then follows the same rules as x does, so using the power rule would result with y2=2y. Why does y2=0 then when I plugin the formula into wolfram?
Wolfram is evaluating a PARTIAL derivative with respect to x. This is not what you want.

4. ## Re: Implicit Differentiation

Originally Posted by Plato
The derivative is $y'=\frac{-x}{y}~.$
$x^2+y^2=4000^2$
$2x+y^2(y')=0$
so I get $y'=\frac{-2x}{y^2}$ how is it you arrived at your answer? I doesn't really matter much anyways because the answer to my problem used the derivative in the form of $y=\sqrt{4000^2-x^2}$ anyways. I think you are dividing by 2y instead of y2, How is that a derivative when it is y2=?
$x^2+y^2=4000^2$
$2x+y^2(y')=0$
It should be $2x+2(y)y'=0$