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

1 Answer
Jake M.
Mar 31, 2018

#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) #

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