240. Find $y^{\prime}$, if $y=\sin ^{2} 4 x$.
Solution. We have $y=\sin ^{2} 4 x$ (3). The order of functions: $y=u^{2} ; u=\sin v ; v=4 x$. Therefore,

$y^{\prime}=2 \sin 4 x(\sin 4 x)^{\prime}=2 \sin 4 x \cos 4 x \cdot(4 x)^{\prime}=2 \sin 4 x \cos 4 x \cdot 4=4 \sin 8 x$ (in the final expression, the double-angle sine formula is used).

In the future, when sufficient experience in differentiation is accumulated, intermediate records can be dispensed with.

For example, if $y=\sin \left(x^{2}+1\right)$, then $y^{\prime}=\cos \left(x^{2}+1\right) \cdot 2 x=$ $=2 x \cos \left(x^{2}+1\right)$.

241-246. Find the derivatives of the following functions: