Find the first partial derivatives of the function fx y x5y

Find the first partial derivatives of the function.

f(x, y) = x⁵y⁶ + 9x²y

f_x(x, y) =

f_y(x, y) =

Solution

The given function is

f(x, y) = x⁵y⁶ + 9 x²y

Partially differentiating f(x,y) with respect to x treating y as constant, we get

f_x(x, y) = 5 x⁴y⁶ + 18 xy, and

Partially differentiating f(x,y) with respect to y treating x as constant, we get

f_y(x, y) = 6 x⁵y⁵ + 9 x²,