My Math Forum Derivatives

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 March 8th, 2010, 08:17 PM #1 Newbie   Joined: Mar 2010 Posts: 2 Thanks: 0 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.
 March 8th, 2010, 11:56 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,302 Thanks: 1972 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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