Question

What is the correct way to solve this problem? Thank you.

Answer 1

`dy/dx = 2xcos^3x(cosx-2xsinx)`

Explanation:

We have:

`y = x^2cos^4x`

We can differentiate wrt `x` using the product rule and the chain rule to get:

`dy/dx = (x^2)(d/dx cos^4x) + (d/dx x^2)(cos^4x)`

`\ \ \ \ \ = (x^2)(4cos^3xd/dxcosx) + (2x)(cos^4x)`

`\ \ \ \ \ = (x^2)(4cos^3x)(-sinx) + (2x)(cos^4x)`

`\ \ \ \ \ = 2xcos^4x - 4x^2cos^3xsinx`

`\ \ \ \ \ = 2xcos^3x(cosx-2xsinx)`