# How do you differentiate arctan(sinx)?

$y ' = \frac{1}{1 + {\sin}^{2} x} \cos x$
The derivative of arctan u is $\frac{1}{1 + {u}^{2}}$. When u is $\sin \left(x\right)$ it is simply $\frac{1}{1 + {\sin}^{2} x}$. The derivative of $\sin \left(x\right)$ is $\cos x$. Multiplying both yields
$y ' = \frac{1}{1 + {\sin}^{2} x} \cos x$