Question

What is the derivative of `sin(4x)`?

Answer 1

`4cos(4x)`

Explanation:

We are dealing with a composite function here, so it helps to use the Chain Rule

`f'(g(x))*g'(x)`

Our function is essentially in the form `f(g(x))`

where `f(x)=sinx` and `g(x)=4x`

Let's find the derivatives and plug into the Chain Rule:

`f'(x)=cosx`, `g'(x)=4`

We have both of our functions and derivatives, now let's plug in:

`cos(4x)*4`

`color(steelblue)(4cos(4x))`

Hope this helps!