Question

How do you find the derivative of `cos(1-2x)^2`?

Answer 1

`4(1-2x)sin(1-2x^2`

Explanation:

Use the chain rule multiple times.

The first issue is the cosine function.

The chain rule states that `d/dx[cos(u)]=-sin(u)*u'`

`d/dx[cos(1-2x)^2]=-sin(1-2x)^2*d/dx[(1-2x)^2]`

The second issue is the squared term.

The chain rule states that `d/dx[u^2]=2u*u'`

`d/dx[(1-2x)^2]=2(1-2x)d/dx[1-2x]`

Since `d/dx[1-2x]=-2`,

`d/dx[cos(1-2x)^2]=-sin(1-2x)2*2(1-2x)(-2)`

`=4(1-2x)sin(1-2x)^2`