Question

Find the general formula for the derivative of function y = cos(2x)

Answer 1

What I did

1. -2sin2x
2. -4cos2x
3.8six2x
4.16cos2x
5.-32cos2x
6.-64sin2x....etc

so I found

2, -2, 2, -2, pattern.

Answer 2

Using the chain rule:

u(x) = 2x

y(u) = cos(u)

The chain rule is:

dy/dx = (dy/du)(du/dx)

dy/du = -sin(u)

du/dx = 2

dy/dx = -sin(u) * 2

u = 2x

dy/dx = -2sin(2x)

Answer 3

I am looking for \[\frac{d^{n}}{dx^{n}} \]