(d^3)/(d{y)d{x}^2}(({f}(y,x))(2{x}^3+{x}^2{y}^4-5{y}^2))

解

\frac{d ^{3}}{d y d x ^{2}} ((f (y, x)) (2 x^{3} + x^{2} y^{4} - 5 y^{2}))

f (y, x) (0 + 8 y^{3} - 0)

解答ステップ

\frac{d ^{3}}{d y d x ^{2}} ((f (y, x)) (2 x^{3} + x^{2} y^{4} - 5 y^{2}))

\frac{d}{d y} (f (y, x) (2 x^{3} + x^{2} y^{4} - 5 y^{2})) = f (y, x) (0 + 4 y^{3} x^{2} - 10 y)

= \frac{d ^{2}}{d x ^{2}} (f (y, x) (0 + 4 y^{3} x^{2} - 10 y))

\frac{d}{d x} (f (y, x) (0 + 4 y^{3} x^{2} - 10 y)) = f (y, x) (0 + 8 x y^{3} - 0)

= \frac{d}{d x} (f (y, x) (0 + 8 x y^{3} - 0))

\frac{d}{d x} (f (y, x) (0 + 8 x y^{3} - 0)) = f (y, x) (0 + 8 y^{3} - 0)

= f (y, x) (0 + 8 y^{3} - 0)