Question

How do you differentiate `f(x)= 5/x^3 - 3/ x^(1/3)`?

Answer 1

`color(blue)(f'(x) = -15/x^4 + 1/x^(4/3)`

Explanation:

`f(x) = 5/x^3 - 3 / x^(1/3)`

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

`(d/(dx)) x^n = n * x^(n-1)`

`:. f'(x) = 5 * -3 * x^-4 - 3 * -(1/3) * x ^-(4/3)`

`f'(x) = -15 x^-4 + x^-(4/3)`

`=> -15/x^4 + 1/x^(4/3)`