Question

find the second derivative of the function. (f(x)=x^{2}+4x^{-3}) (f(x)=)

Explanation:

Step1: Find first - derivative

Use power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$.
$f(x)=x^{2}+4x^{-3}$
$f^\prime(x)=\frac{d}{dx}(x^{2})+\frac{d}{dx}(4x^{-3})=2x+4\times(-3)x^{-4}=2x - 12x^{-4}$

Step2: Find second - derivative

Differentiate $f^\prime(x)$ again using power rule.
$f^{\prime\prime}(x)=\frac{d}{dx}(2x)-\frac{d}{dx}(12x^{-4})=2-12\times(-4)x^{-5}=2 + 48x^{-5}$

Answer:

$2+\frac{48}{x^{5}}$