Calculate the first and second derivative of the following: cos[x] + xsin[x]^2?

Question

Could someone please provide all the steps to working these problems please!!!!

Answer 1

d(cos[x])/dx = -sin[x] and d(sin[x])/dx = cos[x]

First derivative (Using product rule on xsin[x]^2):

= -sin[x] + x*(2xcos[x]^2) + sin[x]^2
= -sin[x] + 2x^2(cos[x]^2) + sin[x]^2

Second derivative from the expression we found

= -cos[x] + 2x^2(-2xsin[x]^2) + 4x(cos[x]^2) + 2x(cos[x]^2)
= 6x(cos[x]^2) - cos[x] - 4x^3(sin[x]^2)

Answer 2

im sure you can do the 1st and second deravitve on the cos(x)
as for xsin(x)^2 use the chain rule