Answer
$$\frac{\partial z}{\partial x}=\cos(x+2y)$$
$$\frac{\partial z}{\partial y}=2\cos(x+2y)$$
Work Step by Step
We will use chain rule to find both partial derivatives.
The partial derivative with respect to $x$ is:
$$\frac{\partial z}{\partial x}=\frac{\partial }{\partial x}(\sin(x+2y))=\cos(x+2y)\frac{\partial }{\partial x}(x+2y)=\cos(x+2y)\cdot1=\cos(x+2y)$$
Here $y$ is treated as a constant.
The partial derivative with respect to $y$ is:
$$\frac{\partial z}{\partial y}=\frac{\partial }{\partial y}(\sin(x+2y))=\cos(x+2y)\frac{\partial }{\partial y}(x+2y)=\cos(x+2y)\cdot2=2\cos(x+2y)$$
because now we $x$ treated as a constant.
