Question

If f(x) = (cos(√x) - In(x^2))^3, then f(x)=

Answer 1

f'(x) = [ 3(cos(√x) - In(x^2))^2 (-√x sin(√x) - 4) ] / 2x

Explanation:

f(x) = y = (cos(√x) - In(x^2))^3

Let u = cos(√x) - In(x^2)

dy/du = 3u^2

= 3(cos(√x) - In(x^2))^2

du/dx = -sin(√x)*1/2x^-1/2 - 2x* 1/x^2

= -sin(√x) * 1/2√x - 2/x

= (-√x sin(√x) - 4)/ 2x

So:

dy/dx = dy/du * du /dx

f'(x) = [ 3(cos(√x) - In(x^2))^2 (-√x sin(√x) - 4) ] / 2x