(d^2)/(dx^2)(({f}(x,z,y))(z^3-2xz+y))

解

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

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

解答ステップ

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

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

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

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

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