Find the first partial derivatives of the function. f(x, y) = x²y?

Solution:

Given f(x, y) = x²y

This is an implicit function which means y can not be written in terms of x

The implicit differentiation is also called partial derivatives means, we differentiate w.r.t one variable keeping the other constant

f’(x, y) = f’_x(x, y) + f’_y(x, y)

f’_x = 2xy

f’_y =  x²

f'(x, y) = 2xy + x²

Thus the first partial derivative of f(x,y ) = 2xy + x²

Find the first partial derivatives of the function. f(x, y) = x²y?

Summary:

The first partial derivatives of the function. f(x, y) = x²y isf’(x, y) = 2xy + x².