Find the derivative.
-$y=\frac{9 e^{x}}{2 e^{x}+1}$
A) $\frac{e^{x}}{\left(2 e^{x}+1\right)^{2}}$
B) $\frac{9 e^{x}}{\left(2 e^{x}+1\right)^{3}}$
C) $\frac{9 e^{x}}{\left(2 e^{x}+1\right)^{2}}$
D) $\frac{9 e^{x}}{\left(2 e^{x}+1\right)}$

Question

Quizplus · Accepted Answer

The derivative is found using the quotient rule: $\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{v \cdot u' - u \cdot v'}{v^2}$. Here, $u = 9e^x$ and $v = 2e^x + 1$. The derivative is $\frac{(2e^x + 1)(9e^x) - (9e^x)(2e^x)}{(2e^x + 1)^2} = \frac{9e^x}{(2e^x + 1)^2}$.

Find the Derivative y=9ex2ex+1y=\frac{9 e^{x}}{2 e^{x}+1}y=2ex+19ex​ A) ex(2ex+1)2\frac{e^{x}}{\left(2 e^{x}+1\right)^{2}}(2ex+1)2ex​ B) 9ex(2ex+1)3\frac{9 e^{x}}{\left(2 e^{x}+1\right)^{3}}(2ex+1)39ex​

Find the Derivative $y=\frac{9 e^{x}}{2 e^{x}+1}$ A) $\frac{e^{x}}{\left(2 e^{x}+1\right)^{2}}$ B) $\frac{9 e^{x}}{\left(2 e^{x}+1\right)^{3}}$