If , then at…

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

Problem

y(\alpha) = \sqrt{2 \left( \frac{\tan \alpha + \cot \alpha}{1 + \tan^2 \alpha} \right) + \frac{1}{\sin^2 \alpha}}

\alpha \in \left( \frac{3\pi}{4}, \pi \right)

then

\frac{dy}{d\alpha}

\alpha = \frac{5\pi}{6}

is (a) 4 (b) 2 (c) 3 (d) -4

Related theory

Trigonometric Identities
Trigonometric Functions
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability
Differentiation Rules

Browse the problem library