Question

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

Answer 1

`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)`