What do you mean by "help"? Tell you what "divergence" and "curl" of a vector function mean? Okay but I am surprised that your teacher didn't tell you that, or your text book did not have the definitions, before you were given this problem!
Given a "vector valued function", \(\displaystyle \vec{F}= f(x,y,z)\vec{i}+ g(x,y,z)\vec{j}+ h(x,y,z)\vec{k}\), where f, g, and h are differentiable functions of the three independent variables, x, y, and z, the "divergence" of \(\displaystyle \vec{F}\) (also denoted by "div \(\displaystyle \vec{F}\)" or \(\displaystyle \nabla\cdot\vec{F}\) is given by \(\displaystyle \frac{\partial f}{\partial x}+ \frac{\partial g}{\partial y}+ \frac{\partial h}{\partial z}\). If we think of "\(\displaystyle \nabla\)" as the (purely symbolic) "vector operator" \(\displaystyle \frac{\partial}{\partial x}\vec{i}+ \frac{\partial}{\partial y}\vec{j}+ \frac{\partial}{\partial z}\vec{k}\), then divergence of \(\displaystyle \vec{F}\) can be thought of as the "dot product" of \(\displaystyle \nabla\) and \(\displaystyle \vec{F}\).
In this problem, \(\displaystyle f(x,y,z)= x cos(\pi y)\). What is \(\displaystyle \frac{\partial f}{\partial x}\)? \(\displaystyle g(x,y,z)= \frac{2x^2}{\pi}sin(\pi y)- 2y^2e^{-z}\). What is \(\displaystyle \frac{\partial g}{\partial y}\)? And \(\displaystyle h(x,y,z)= ye^{-z}\). What is \(\displaystyle \frac{\partial h}{\partial z}\)?
The "curl" is a little more complicated! Given the same \(\displaystyle \vec{F}\) as above, \(\displaystyle curl \vec{F}= \left(\frac{\partial h}{\partial y}- \frac{\partial g}{\partial z}\right)\vec{i}+\)\(\displaystyle \left(\frac{\partial f}{\partial z}- \frac{\partial h}{\partial x}\right)\vec{j}+ \)\(\displaystyle \left(\frac{\partial g}{\partial x}- \frac{\partial f}{\partial y}\vec{k}\right)\).
That can be thought of as the "cross product" of the "vector operator", \(\displaystyle \nabla\), and the vector function \(\displaystyle \vec{F}\), and conveniently remembered as the (symbolic) determinant \(\displaystyle \left|\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ f(x,y,z) & g(x,y,z) & h(x,y,z) \end{array}\right|\).