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)