find f(x). f(x)=4x^2 - 15x - 7/x^4

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=4x^{2}-15x - 7x^{-4}$.

Step2: Find the first - derivative

Using the power rule $(x^n)'=nx^{n - 1}$, we have $f'(x)=(4x^{2})'-(15x)'-(7x^{-4})'=4\times2x-15-7\times(-4)x^{-5}=8x - 15 + 28x^{-5}$.

Step3: Find the second - derivative

Again using the power rule, $f''(x)=(8x)'-(15)'+(28x^{-5})'=8+28\times(-5)x^{-6}=8-\frac{140}{x^{6}}$.

Answer:

$8-\frac{140}{x^{6}}$