What is the derivative of #5arcsin(x^4) #?

1 Answer
Oct 24, 2015

#d/dx[5arcsin(x^4)]=(20x^3)/(sqrt(1-x^8))#

Explanation:

We need to use the chain rule here. We differentiate the #5arcsin( )# part first then multiply that by the derivative of what's inside the brackets.

So:

#d/dx[5arcsin(x^4)]=5d/dx[arcsin(x^4)]#

#=5xx(1)/sqrt(1-(x^(4))^2)xx4x^3#

#=(20x^(3))/(sqrt(1-x^8))#