Question

Let f(x, y)= 4x³y+7xy⁴ . Find fₓₓ, fᵧᵧ, fᵧₓ, and fₓᵧ.

Answer 1

To find fₓₓ, fᵧᵧ, fᵧₓ, and fₓᵧ for the given function, differentiate the function twice with respect to x and y.

Step-by-step explanation:

To find fₓₓ, fᵧᵧ, fᵧₓ, and fₓᵧ for the function f(x, y) = 4x³y+7xy⁴, we will need to differentiate the function twice with respect to x and y.

First, we differentiate f(x, y) with respect to x:

fₓ = 12x²y + 7y⁴

Then, we differentiate fₓ with respect to x:

fₓₓ = 24xy + 0

Next, we differentiate f(x, y) with respect to y:

fᵧ = 4x³ + 28xy³

Finally, we differentiate fᵧ with respect to y:

fᵧᵧ = 12x² + 84xy²