March 8th, 2010, 07:17 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 ?(1u^2) 3) y= z (cos^1) z?(1z^2) Any help would be greatly appreciated. Thanks. 
March 8th, 2010, 10:56 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
1) log(theta) = 2logtheta . . . can you differentiate logtheta? 2) Use the chain rule. 3) Use the chain rule and the fact that the derivative of with respect to x is 1/?(1  x²). 

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