Question

If z = cos (xy) , show that

Short answer

It is proved that

Step-by-step solution

Given information.

Given z = cos (xy)

Definition of partial differentiation.

Partial differentiation is defined as the process, in which find the partial derivative of a function.

In Partial differentiation, the function has more than one variable and find the partial derivative of a function with respect to one variable and keeping the other variable constant.

Calculate ∂z/∂x and ∂z/∂y

Find the partial differentiation of function, z = cos(xy) with respect to x.

Find the partial differentiation of function, z = cos(xy) with respect to y .

Now multiply with x in equation (1) and multiply with y in equation (2).

Subtract equation (4) from equation (3).

Hence it is proved.