Answer
$$\frac{\partial z}{\partial x}=2\cosh(2x+3y)$$
$$\frac{\partial z}{\partial y}=3\cosh(2x+3y)$$
Work Step by Step
We will use chain rule to find both partial derivatives.
The partial derivative with respect to $x$ is:
$$\frac{\partial z}{\partial x}=\frac{\partial }{\partial x}(\sinh(2x+3y))=\cosh(2x+3y)\frac{\partial }{\partial x}(2x+3y)=\cosh(2x+3y)\cdot2=2\cosh(2x+3y)$$
We treated here $y$ as a constant.
The partial derivative with respect to $y$ is:
$$\frac{\partial z}{\partial y}=\frac{\partial }{\partial y}(\sinh(2x+3y))=\cosh(2x+3y)\frac{\partial }{\partial y}(2x+3y)=\cosh(2x+3y)\cdot3=3\cosh(2x+3y)$$
because now is $x$ treated as a constant.
