Hello Nirmal,

From what I can sense your actual question should be like e^x(sin Y). But you've written ex×(sin Y). So, just to be sure I'm going to help you in both the cases.

In the first case; e^x(sin Y) ; for partial difference you'll have to differentiate with respect to x while keeping 'Y' constant. Again differentiating with respect to Y keeping 'x' constant.

du/dx = e^x sinY

du/dy = e^x cosY

Following the same method we can also get the partial difference of function ex×(sinY)

du/dx = e sinY

du/dy = ex× cosY

This is the proper method to get any function's partial derivative!