Question:
\(\dfrac{d}{dx}\big(\sin \tfrac{4x}{5}\big)=\) ?
\(\dfrac{d}{dx}\big(\sin \tfrac{4x}{5}\big)=\) ?
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Always multiply by the inner derivative \(u'\) after differentiating the outside.
Updated On: Oct 17, 2025
- \(\dfrac{4}{5}\cos \tfrac{4x}{5}\)
- \(-\dfrac{4}{5}\cos \tfrac{4x}{5}\)
- \(\dfrac{5}{4}\cos \tfrac{4x}{5}\)
- \(-\dfrac{5}{4}\cos \tfrac{4x}{5}\)
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The Correct Option is A
Solution and Explanation
Chain rule: \((\sin u)'=\cos u\cdot u'\) with \(u=\dfrac{4x}{5}\Rightarrow u'=\dfrac{4}{5}\). So derivative \(=\dfrac{4}{5}\cos\!\left(\dfrac{4x}{5}\right)\).
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