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