what is the derivative of cos^3(x+1)?

Question

please help

Answer 1

3 cos^2(x+1)*(-sin(x+1))

Answer 2

This is by general power rule:
Bring down the power, subtract one from the power and multiply by the derivative of the inside function.

3 cos^2(x+1) * - sin(x+1)

= -3 cos^2(x+1) sin(x+1)

Answer 3

Use the chain rule:

du^3/du = 3u² (u is cos)

dcos u/du = -sin u (u is x+1)

d(x+1)/dx = 1

then put them together:

3cos² (x+1) • -sin (x+1) • 1 =
-3cos² (x+1) sin (x+1)

Answer 4

dy/dx cos^3(x+1)
u = x +1
du/dx = 1
dv/du = -sin(x+1)
dy/dv = 3cos^2(x+1)

dy/dx = 3cos^2(x+1) X -sin(x+1)