Derivative of SQRT(X + Sin^2 (3x) )

[ur5pointos2sl]

The original equation is as follows: SQRT(X + Sin^2 (3x) )... I tried to work it out and got the answer to be: 3(X+sin^2(3x)) ( X + sin(3x)) can someone verify if this is right or wrong for me please? Sorry I can't use code to type these problems. Thanks

 

[jacobrhcp]

so make repeated use of the chain rule. Step one is to wonder what the derivative of sqrt(y) is? then go on to work out [sqrt(y)]' * y', where of course the first derivative is with respect to y, and the second with respect to some x on which y depends.

then treat y' as a whole new problem, and forget what you've done thus far for the moment.

I'll start you up:

derivative =[1/2(sqrt(x+sin^2(3x))] * [x+sin^2(3x)]'

and now repeat, what is the next rule first? sum rule or chain rule? and after that? and after that again?