Question

find the indicated derivative for the function.
h(x) for h(x)=5x^{-7}-2x^{-8}
h(x)=\square

Explanation:

Step1: Find the first - derivative

Use the power rule \((x^n)^\prime=nx^{n - 1}\).
For \(y = 5x^{-7}-2x^{-8}\), the first - derivative \(h^\prime(x)\) is:
\(h^\prime(x)=5\times(-7)x^{-7 - 1}-2\times(-8)x^{-8 - 1}\)
\(h^\prime(x)=-35x^{-8}+16x^{-9}\)

Step2: Find the second - derivative

Differentiate \(h^\prime(x)=-35x^{-8}+16x^{-9}\) again using the power rule.
\(h^{\prime\prime}(x)=-35\times(-8)x^{-8 - 1}+16\times(-9)x^{-9 - 1}\)
\(h^{\prime\prime}(x)=280x^{-9}-144x^{-10}\)
\(h^{\prime\prime}(x)=\frac{280}{x^{9}}-\frac{144}{x^{10}}\)

Answer:

\(\frac{280}{x^{9}}-\frac{144}{x^{10}}\)