How do you find the derivative of #y=3/4(x^(2)-1)^(2/3)#?

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Answer 1 · 2016-02-27T13:18:04

#f'(x)=x/root(3)(x^2-1)#

#f(x)=3/4(x^2-1)^(2/3)#

Derivative:
#f'(x)=3/4*2/3*(x^2-1)^(-1/3)*2x#

#color(blue)(f'(x)=x/root(3)(x^2-1))#

Steps:

#1" "# #3/4# is a constant so we can bring that out.

#2" "# Using Power Rule, we can get #2/3(x^2-1)^(-1/3)#. However, since #(x^2-1)# isn't #x#, we have to use Chain Rule.

#3" "# We get the derivative of #(x^2-1)# which is #2x# and multiply it.

Sorry, I'm not very good at explaining this. Just let me know if you have questions.