For , the function is decreasing. Explain in one or two sentences why the sign of…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For

0 < x < \pi/2

, the function

\cot x

is decreasing. Explain in one or two sentences why the sign of

\dfrac{d}{dx}(\cot x)

must be negative on this interval, referring only to the signs of

\sin x

and

\cos x

Related theory

Increasing and Decreasing Functions
Curve Analysis
Differentiation Rules
Derivatives of standard functions via chain rule

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