Question

find the indicated derivative for the function. h(x) for h(x)=2x^{-4}-6x^{-6}

Explanation:

Step1: Find the first - derivative

Use the power rule $\frac{d}{dx}(ax^n)=nax^{n - 1}$. For $h(x)=2x^{-4}-6x^{-6}$, $h'(x)=2\times(-4)x^{-4 - 1}-6\times(-6)x^{-6 - 1}=-8x^{-5}+36x^{-7}$.

Step2: Find the second - derivative

Apply the power rule again on $h'(x)$. $h''(x)=(-8)\times(-5)x^{-5 - 1}+36\times(-7)x^{-7 - 1}=40x^{-6}-252x^{-8}$.

Answer:

$h''(x)=40x^{-6}-252x^{-8}$