Find the derivative of the function $\sin^{n} x$ with respect to $x$,where $n$ is an integer.

(N/A) Let $y = \sin^{n} x$.
Using the chain rule for differentiation,we treat $\sin^{n} x$ as a composite function $f(g(x))$,where $f(u) = u^{n}$ and $g(x) = \sin x$.
According to the chain rule,$\frac{dy}{dx} = \frac{df}{du} \cdot \frac{du}{dx}$.
Here,$\frac{df}{du} = n u^{n-1} = n(\sin x)^{n-1}$ and $\frac{du}{dx} = \frac{d}{dx}(\sin x) = \cos x$.
Therefore,$\frac{dy}{dx} = n(\sin x)^{n-1} \cdot \cos x$.
Hence,$\frac{d}{dx}(\sin^{n} x) = n \sin^{n-1} x \cos x$.