Find the first partial derivatives of the function. f(x, y) = x³y

Solution:

Given f(x,y) = x³y

This is an implicit function where we can not separate y from x

The partial derivative means the function will be in both x,y , first we need to differentiate w.r.t x keeping y constant and then differentiate w.r.t y keeping x constant.

\(\frac{\partial f(x,y)}{\partial x}\) = 3x²(y) + x³ dy/dx

The first partial derivatives of the function. f(x, y) = x³y is 3x²(y) + x³ dy/dx

Find the first partial derivatives of the function. f(x, y) = x³y

Summary:

The first partial derivatives of the function. f(x, y) = x³y is 3x²(y) + x³dy/dx