# How do you find the derivative for k(x) = sin (x^2+2)?

Using the chain rule, which states that the derivative of $f \left(g \left(x\right)\right)$ is $f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$. In your case, the outer function $f \left(x\right)$ is $\setminus \sin \left(x\right)$, and the inner function $g \left(x\right)$ is ${x}^{2} + 2$.
This means that $f ' \left(x\right) = \setminus \cos \left(x\right)$, and $g ' \left(x\right) = 2 x$.
$\frac{d}{\mathrm{dx}} \sin \left({x}^{2} + 2\right) = \setminus \cos \left({x}^{2} + 2\right) \cdot 2 x$