Find the first partial derivatives of the function. f(x, y) = x⁷y?

Solution:

Given function is

f(x, y) = x⁷y

Since, it is an implicit function, we need to do implicit differentiation by finding partial derivatives

Partial derivative means differentiating w.r.t one variable keeping the other as a constant.

d(f(x, y)) = d(f(x, y))/dx + d(f(x, y))/dy

d(f(x, y)) = 7x⁶y + x⁷dy/dx

Hence, the partial derivative of the given implicit function is 7x⁶y + x⁷dy/dx

Find the first partial derivatives of the function. f(x, y) = x⁷y?

Summary:

The first partial derivatives of the function. f(x, y) = x⁷y is 7x⁶y + x⁷dy/dx