Question

find f(x).
f(x)=4x^{2}-15x - \frac{5}{x^{4}}
f(x)=square

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=4x^{2}-15x - \frac{5}{x^{4}}$ as $f(x)=4x^{2}-15x-5x^{-4}$.

Step2: Find the first - derivative

Use the power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$.
$f'(x)=\frac{d}{dx}(4x^{2})-\frac{d}{dx}(15x)-\frac{d}{dx}(5x^{-4})$.
$f'(x)=4\times2x-15-5\times(-4)x^{-5}=8x - 15 + 20x^{-5}$.

Step3: Find the second - derivative

Differentiate $f'(x)$ again using the power rule.
$f''(x)=\frac{d}{dx}(8x)-\frac{d}{dx}(15)+\frac{d}{dx}(20x^{-5})$.
$f''(x)=8-0+20\times(-5)x^{-6}=8 - 100x^{-6}=8-\frac{100}{x^{6}}$.

Answer:

$8-\frac{100}{x^{6}}$