Question

\(\dfrac{d}{dx}\big(\sin \tfrac{4x}{5}\big)=\) ?

• A. \(\dfrac{4}{5}\cos \tfrac{4x}{5}\)
• B. \(-\dfrac{4}{5}\cos \tfrac{4x}{5}\)
• C. \(\dfrac{5}{4}\cos \tfrac{4x}{5}\)
• D. \(-\dfrac{5}{4}\cos \tfrac{4x}{5}\)

Hint:

Always multiply by the inner derivative \(u'\) after differentiating the outside.

Answer 1

The Correct Option is A

Chain rule: \((\sin u)'=\cos u\cdot u'\) with \(u=\dfrac{4x}{5}\Rightarrow u'=\dfrac{4}{5}\). So derivative \(=\dfrac{4}{5}\cos\!\left(\dfrac{4x}{5}\right)\).