AP

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Determine

\displaystyle \lim_{x\to 0} \dfrac{\sin\!\left(\tfrac{\pi}{4}+3x\right)-\sin\!\left(\tfrac{\pi}{4}\right)}{x}

. (a)

3

(b)

\dfrac{3\sqrt{2}}{2}

(c)

-\dfrac{3\sqrt{2}}{2}

(d)

\dfrac{\sqrt{2}}{2}

Related theory

Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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