(d^2)/(dx^2)(9z^2e^z)

解

\frac{d ^{2}}{d x ^{2}} (9 z (x)^{2} e^{z (x)})

9 (2 e^{z} \frac{d z}{d x}^{2} + 4 e^{z} z \frac{d z}{d x}^{2} + e^{z} z^{2} \frac{d z}{d x}^{2} + 2 e^{z} z \frac{d ^{2} z}{d x ^{2}} + e^{z} z^{2} \frac{d ^{2} z}{d x ^{2}})

解答ステップ

\frac{d ^{2}}{d x ^{2}} (9 z^{2} e^{z})

\frac{d}{d x} (9 z^{2} e^{z}) = 9 (2 z \frac{d z}{d x} e^{z} + e^{z} \frac{d z}{d x} z^{2})

= \frac{d}{d x} (9 (2 z \frac{d z}{d x} e^{z} + e^{z} \frac{d z}{d x} z^{2}))

\frac{d}{d x} (9 (2 z \frac{d z}{d x} e^{z} + e^{z} \frac{d z}{d x} z^{2})) = 9 (2 e^{z} \frac{d z}{d x}^{2} + 4 e^{z} z \frac{d z}{d x}^{2} + e^{z} z^{2} \frac{d z}{d x}^{2} + 2 e^{z} z \frac{d ^{2} z}{d x ^{2}} + e^{z} z^{2} \frac{d ^{2} z}{d x ^{2}})

= 9 (2 e^{z} \frac{d z}{d x}^{2} + 4 e^{z} z \frac{d z}{d x}^{2} + e^{z} z^{2} \frac{d z}{d x}^{2} + 2 e^{z} z \frac{d ^{2} z}{d x ^{2}} + e^{z} z^{2} \frac{d ^{2} z}{d x ^{2}})