Let be a differentiable function of satisfying for and

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let

y

be a differentiable function of

x

satisfying

\ln(xy)=x^{2}

for

x>0

and

y>0

. What is

\dfrac{dy}{dx}

at the point

(1,e)

? (a)

2e

(b)

e

(c)

1

(d)

e^{2}

Related theory

Advanced Differentiation
Implicit and Parametric Differentiation
Derivatives of implicit functions
Continuity and Differentiability

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