Derivative Help

[clannkelly]

Could somebody give me a step by step rundown?

Differentiate using the chain rule. The original equation is x^2 + y^2 = 25

So far, I've got:

1/2*(25-x^2)^-1/2 * (2x)

which apparently turns into

The book isn't telling me how to get from step to step, it's just showing me. I can't seem to figure out the algebra for this one.

 

[pka]

Could somebody give me a step by step rundown?
Differentiate using the chain rule. The original equation is
\(\displaystyle x^2 + y^2 = 25\)

Use implicit differentiation.
\(\displaystyle 2x+2yy'=0\) solve for \(\displaystyle y'\).

 

[HallsofIvy]

"Implicit differentiation", which pka suggests, uses the chain rule, referred to in the problem:
The derivative of \(\displaystyle y^2\), with respect to x, is the derivative of \(\displaystyle y^2\) with respect to y, times the derivative of y with respect to x. The derivative of \(\displaystyle y^2\) is, of course, 2y, and while we do not know the exact form of y as a function of x, we can write it as y'.