Procedures for Calculating Derivatives

AP Calculus AB· difficulty 4/5

If y=xxy = x^x, then dydx\dfrac{dy}{dx} at x=1x = 1 equals

  • A

    ee

  • B

    00

  • C

    ln2\ln 2

  • D

    11

    check_circle

Explanation

lny=xlnx\ln y = x\ln x. Differentiate to get y/y=lnx+1y'/y = \ln x + 1, hence y=xx(lnx+1)y' = x^x(\ln x + 1). At x=1x=1: y=1(0+1)=1y' = 1 \cdot (0+1) = 1.

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