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 takuto March 8th, 2010 07:17 PM

Derivatives

Hi. I'm having some problems with doing derivatives. I have some of the answers for my homework, but I am stuck on others.

For example, I know how to get the derivative of this problem: y=x^(ln(x))
y=x^(ln(x))
ln(y)=ln(x^(ln(x))
ln(y)=ln(x)ln(x)
implicit differentiation+product rule yields
(1/y)y'=(1/x)ln(x)+(1/x)ln(x)
(1/y)y'=(2/x)ln(x)
y'=(2/x)yln(x)
=(2yln(x))/x

However, I'm having problems finding derivatives for:

1) y=log (theta^2)
2) y=sin ?(1-u^2)
3) y= z (cos^-1) z-?(1-z^2)

Any help would be greatly appreciated. Thanks.

 skipjack March 8th, 2010 10:56 PM

1)  log(theta) = 2log|theta| . . . can you differentiate log|theta|?

2)  Use the chain rule.

3) Use the chain rule and the fact that the derivative of $^{\cos^{-1}x}$ with respect to x is -1/?(1 - x²).

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