Using the property of derivative differentiate? #root5(x^3)#

1 Answer
Feb 26, 2018

#f'(x)=3/5x^(-2/5)#

Explanation:

We want to find the derivative of

#f(x)=root(5)(x^3)=x^(3/5)#

A property/rule for derivatives is the power rule

It states if #f(x)=x^(color(blue)(n))# then #f'(x)=color(blue)nx^(color(blue)(n)-1)#

Just like we have in our example for #n=3/5#

Thus

#f'(x)=3/5x^(3/5-1)=3/5x^(-2/5)#