Find the derivative of the function.
-$f(x)=\frac{1}{\left(x^{7}+2\right)^{2}}$
A) $f^{\prime}(x)=\frac{14 x^{6}}{\left(x^{7}+2\right)^{2}}$
B) $f^{\prime}(x)=-\frac{7 x^{6}}{\left(x^{7}+2\right)^{2}}$
C) $f^{\prime}(x)=-\frac{14 x^{6}}{\left(x^{7}+2\right)^{3}}$
D) $f^{\prime}(x)=\frac{7 x^{6}}{\left(x^{7}+2\right)^{3}}$

Question

Quizplus · Accepted Answer

The derivative is found using the chain rule and the power rule. The function is of the form $u^{-2}$ where $u = x^7 + 2$. The derivative is $-2u^{-3} \cdot u'$, where $u' = 7x^6$. Thus, the derivative is $-\frac{14x^6}{(x^7+2)^3}$.