Which of the following expressions is the derivative of for ?

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Which of the following expressions is the derivative of h(x)=e3xln⁡xh(x)=\dfrac{e^{3x}}{\ln x} for x>0x>0? (a) e3x(3ln⁡x−1/x)ln⁡x\displaystyle \frac{e^{3x}\bigl(3\ln x-1/x\bigr)}{\ln x} (b) e3x(3ln⁡x−1x)(ln⁡x)2\displaystyle \frac{e^{3x}\bigl(3\ln x-\tfrac1x\bigr)}{(\ln x)^2} (c) e3x(3ln⁡x+1/x)(ln⁡x)2\displaystyle \frac{e^{3x}\bigl(3\ln x+1/x\bigr)}{(\ln x)^2} (d) 3e3xln⁡x\displaystyle \frac{3e^{3x}}{\ln x}

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