The curve is defined by and

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The curve is defined by x=etx=e^{t} and y=ln⁡ty=\ln t. After eliminating the parameter tt, which of the following expressions equals dydx\dfrac{dy}{dx} in terms of xx alone? (a) 1x(ln⁡x)2\dfrac{1}{x(\ln x)^{2}} (b) 1x ln⁡x\dfrac{1}{x\,\ln x} (c) ln⁡xx\dfrac{\ln x}{x} (d) 1x\dfrac{1}{x}

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