find the indicated derivative for the function. \n$h(x)$ for $h(x)=7x^{-2}-8x^{-6}$\n$h(x)=\\square$

Explanation:

Step1: Find the first - derivative

Use the power rule ((x^n)^\prime=nx^{n - 1}). For (h(x)=7x^{-2}-8x^{-6}), (h^\prime(x)=7\times(-2)x^{-2 - 1}-8\times(-6)x^{-6 - 1}) (h^\prime(x)=-14x^{-3}+48x^{-7})

Step2: Find the second - derivative

Differentiate (h^\prime(x)) again using the power rule. (h^{\prime\prime}(x)=-14\times(-3)x^{-3 - 1}+48\times(-7)x^{-7 - 1}) (h^{\prime\prime}(x)=42x^{-4}-336x^{-8})

Step3: Find the third - derivative

Differentiate (h^{\prime\prime}(x)) using the power rule. (h^{\prime\prime\prime}(x)=42\times(-4)x^{-4 - 1}-336\times(-8)x^{-8 - 1}) (h^{\prime\prime\prime}(x)=-168x^{-5}+2688x^{-9}) (h^{\prime\prime\prime}(x)=-\frac{168}{x^{5}}+\frac{2688}{x^{9}})

Answer:

(-\frac{168}{x^{5}}+\frac{2688}{x^{9}})