find f(x). f(x)=3x^2 - 15x - 4/x^3 f(x)=□

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=3x^{2}-15x - \frac{4}{x^{3}}$ as $f(x)=3x^{2}-15x - 4x^{-3}$.

Step2: Find the first - derivative

Use the power rule $(x^n)'=nx^{n - 1}$. $f'(x)=(3x^{2})'-(15x)'-(4x^{-3})'=3\times2x-15-4\times(-3)x^{-4}=6x - 15+12x^{-4}$.

Step3: Find the second - derivative

Differentiate $f'(x)$ again using the power rule. $f''(x)=(6x)'-(15)'+(12x^{-4})'=6+12\times(-4)x^{-5}=6-\frac{48}{x^{5}}$.

Answer:

$6-\frac{48}{x^{5}}$