Question

How do you find the derivative of `cos^6(2x+5)`?

Answer 1

Applying chain rule for differentiation as follows

`\frac{d}{dx}\cos^6(2x+5)`

`=\frac{d}{dx}(\cos(2x+5))^6`

`=6(\cos(2x+5))^5\frac{d}{dx}(\cos(2x+5))`

`=6\cos^5(2x+5)(-\sin(2x+5))\frac{d}{dx}(2x+5)`

`=-6\sin(2x+5)\cos^5(2x+5)(2)`

`=-12\sin(2x+5)\cos^5(2x+5)`