Derivative Help

clannkelly

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Joined
Jan 29, 2012
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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

symimage.cgi


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.
 
Could somebody give me a step by step rundown?
Differentiate using the chain rule. The original equation is
x2+y2=25\displaystyle x^2 + y^2 = 25
Use implicit differentiation.
2x+2yy=0\displaystyle 2x+2yy'=0 solve for y\displaystyle y'.
 
"Implicit differentiation", which pka suggests, uses the chain rule, referred to in the problem:
The derivative of y2\displaystyle y^2, with respect to x, is the derivative of y2\displaystyle y^2 with respect to y, times the derivative of y with respect to x. The derivative of y2\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'.
 
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