Calculus find f_yxy answer?

When getting the partial derivative with respect to x, treat y as a constant, and visa-versa.

This is asking you to get the derivative with respect to y, first, then get the derivative of that with respect to x, then get the derivative with respect to y of that to get the final function:

f(x, y) = x⁷y⁴ - 7x⁸y + x

f_y = 4x⁷y³ - 7x⁸

f_yx = 28x⁶y³ - 56x⁷

f_yxy = 84x⁶y²

f(x,y) = x^7 y^4 - 7x^8 y+x

f_ʸˣʸ = (f_y)_ˣʸ

        = (4x⁷y³ - 7x⁸)_ˣʸ

        =  (28x⁶y³ - 56x⁷)_ʸ

        =  84x⁶y²  .......................ANS