Find the derivative: y=sin(x^2)cos(x^2), y=cos^3(12theta) (using chain rule)?

Question

1. y=sin(x^2)cos(x^2) 
2. y=cos^3(12theta) 
The first one i got 2xcos(x^2)-2xsin(x^2) (using the chain rule) but this is wrong too 
i got -sin^3(12theta)*12 for the second one but i think its wrong.

Answer 1

Chain Rule:

Chain rule is defined as a mathametical rule concerning the differentiation of a function of a function (as f[u(x )] ) by which under suitable conditions of continuity and differentiability, one function is differentiated with respect to the second function considered as an independent variable and then the second function is differentiated with respect to its independent variable.

Chain rule allows functions that are composed of one another to be differentiated.

If y = f (u ) and u = g (x ) then the derivative of y is , Leibnitz notation.

1) The function is .

Differentiate with respect to x.

2) The function is  .

Differentiate with respect to θ.