Question

How do you find the derivative of `f(x)=sqrtx-5root3(x)`?

Answer 1

`f'(x) = frac{1-15x}{2sqrt{x}}.`

Using the sum rule, each term can be derived separately.

Explanation:

Changing the surds into indices makes f(x) easier to differentiate:

`f(x) = x^{1/2} - 5*x^{3/2}.`

Using the sum rule, each term can be derived separately:

`f'(x) = (1/2) * x^(-1/2) - 5*(3/2)*x^(1/2).`

`f'(x) = (1/2) * x^(-1/2) - (15/2)*x^(1/2).`

`f'(x) = frac{1-15x}{2sqrt{x}}`