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Single Variable Calculus

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Moderate

A Derivative Requiring the Quotient and Product Rules

SVCALC-FSTYBZ

Find the derivative of the function $f(x)=\dfrac{3+xe^x}{e^x-2x}$.

A

$\dfrac{e^x+xe^x}{e^x-2}$

B

$\dfrac{\left(e^x\right)(e^x-2x) - \left(3+xe^x\right)(e^x-2)}{(e^x-2x)^2}$

C

$\dfrac{\left(e^x+xe^x\right)(e^x-2x) + \left(3+xe^x\right)(e^x-2)}{(e^x-2x)^2}$

D

$\dfrac{\left(e^x+xe^x\right)(e^x-2x) - \left(3+xe^x\right)(e^x-2)}{(e^x-2x)^2}$