AP

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let

y=x^{x}

for

x>0

. (i) Find

\dfrac{dy}{dx}

, expressing your answer in its simplest form. (ii) Hence determine the slope of the curve at the point where

x=1

. (iii) Obtain the equation of the tangent to the curve at this point.

Related theory

Interpreting Derivatives
Logarithmic Differentiation
Advanced Differentiation
Differentiation Rules
Logarithmic differentiation and differentiation of one function w.r.t. another
Continuity and Differentiability

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