Find the derivative of the function.
-$g(x)=\frac{x^{2}+5}{(x+6)^{2}}$
A) $g^{\prime}(x)=\frac{6 x-5}{(x+6)^{3}}$
B) $g^{\prime}(x)=-\frac{12 x-10}{(x+6)^{2}}$
C) $g^{\prime}(x)=\frac{12 x-10}{(x+6)^{3}}$
D) $g^{\prime}(x)=\frac{12 x^{2}-10 x}{(x+6)^{3}}$

Question

Quizplus · Accepted Answer

The derivative is found using the quotient rule: $(\frac{u}{v})' = \frac{u'v - uv'}{v^2}$. Here, $u = x^2 + 5$ and $v = (x+6)^2$. Calculating $u'$ and $v'$, and applying the quotient rule gives the derivative $\frac{12x - 10}{(x+6)^3}$.

Find the Derivative of the Function g(x)=x2+5(x+6)2g(x)=\frac{x^{2}+5}{(x+6)^{2}}g(x)=(x+6)2x2+5​ A) g′(x)=6x−5(x+6)3g^{\prime}(x)=\frac{6 x-5}{(x+6)^{3}}g′(x)=(x+6)36x−5​ B) g′(x)=−12x−10(x+6)2g^{\prime}(x)=-\frac{12 x-10}{(x+6)^{2}}g′(x)=−(x+6)212x−10​

Find the Derivative of the Function $g(x)=\frac{x^{2}+5}{(x+6)^{2}}$ A) $g^{\prime}(x)=\frac{6 x-5}{(x+6)^{3}}$ B) $g^{\prime}(x)=-\frac{12 x-10}{(x+6)^{2}}$