Mathematics

Problem

Which of the following expressions is the derivative of

h(x)=\dfrac{e^{3x}}{\ln x}

for

x>0

? a)

\displaystyle \frac{e^{3x}\bigl(3\ln x-1/x\bigr)}{\ln x}

\displaystyle \frac{e^{3x}\bigl(3\ln x-\tfrac1x\bigr)}{(\ln x)^2}

\displaystyle \frac{e^{3x}\bigl(3\ln x+1/x\bigr)}{(\ln x)^2}

\displaystyle \frac{3e^{3x}}{\ln x}