Derivatives of powers of sine functions

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Find the derivative $\;\;\;\frac{d}{dx}sin^{4}\left(4x+1\right)$

**Answer**

$\;\;\;\frac{d}{dx}sin^{4}\left(4x+1\right)$

$=\left(4\right)\,sin^{3}\left(4x+1\right)\,\left(cos\left(4x+1\right)\right)\,\left(4\right)$

$=16\,sin^{3}\left(4x+1\right)\,cos\left(4x+1\right)$