For the relation with

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

Problem

For the relation

x=\cot y

with

0<y<\dfrac{\pi}{2}

, which statement describes the sign of

\dfrac{dy}{dx}

on this interval? (a)

\dfrac{dy}{dx}

changes sign within the interval. (b)

\dfrac{dy}{dx}

is negative for all such

y

. (c)

\dfrac{dy}{dx}

is positive for all such

y

. (d)

\dfrac{dy}{dx}

equals

0

y=\tfrac{\pi}{2}

and is negative elsewhere in the interval.

Related theory

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

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