find the indicated derivative for the function.\nh(x) for h(x)=6x^{-5}-2x^{-7}\nh(x)=□

Explanation:

Step1: Find the first - derivative

Use the power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$. $h'(x)=\frac{d}{dx}(6x^{-5}-2x^{-7})=6\times(-5)x^{-5 - 1}-2\times(-7)x^{-7 - 1}=-30x^{-6}+14x^{-8}$

Step2: Find the second - derivative

Apply the power rule again on $h'(x)$. $h''(x)=\frac{d}{dx}(-30x^{-6}+14x^{-8})=-30\times(-6)x^{-6 - 1}+14\times(-8)x^{-8 - 1}=180x^{-7}-112x^{-9}$

Answer:

$180x^{-7}-112x^{-9}$