Question

How do you find the derivative of `arcsin^5(4x+4)`?

Answer 1

`d/dx(arcsin^5(4x+4))= (20arcsin^4(4x+4))/sqrt(1-(4x+4)^2)`

Explanation:

Let's take this derivative step by step.

First, we recognize that we need an order to take these in.
We should begin with the power rule by thinking of
`arcsin^5(4x+4) = (arcsin(4x+4))^5`

So we already have
`d/dx(arcsin^5(4x+4)) = d/dx((arcsin(4x+4))^5)`
`= 5 arcsin(4x+4)^4\ d/dx(arcsin(4x+4))`

Now we can use the derivative of arcsine to complete the derivation:

`= 5arcsin(4x+4)^4 * 1/(sqrt(1 - (4x+4)^2)) * d/dx(4x+4)`
`= (20arcsin^4(4x+4))/sqrt(1-(4x+4)^2)`