(d^2)/(dx^2)((e^x+x^pi)(x^2+x+1))

解

\frac{d ^{2}}{d x ^{2}} ((e^{x} + x^{π}) (x^{2} + x + 1))

e^{x} x^{2} + 5 e^{x} x + π^{2} x^{π} + 3 π x^{π} + 2 x^{π} + π^{2} x^{π - 1} + π^{2} x^{π - 2} + π x^{π - 1} - π x^{π - 2} + 5 e^{x}

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((e^{x} + x^{π}) (x^{2} + x + 1))

\frac{d}{d x} ((e^{x} + x^{π}) (x^{2} + x + 1)) = e^{x} x^{2} + 3 e^{x} x + π x^{π} + x^{π} + π x^{π + 1} + π x^{π - 1} + 2 x^{π + 1} + 2 e^{x}

= \frac{d}{d x} (e^{x} x^{2} + 3 e^{x} x + π x^{π} + x^{π} + π x^{π + 1} + π x^{π - 1} + 2 x^{π + 1} + 2 e^{x})

\frac{d}{d x} (e^{x} x^{2} + 3 e^{x} x + π x^{π} + x^{π} + π x^{π + 1} + π x^{π - 1} + 2 x^{π + 1} + 2 e^{x}) = e^{x} x^{2} + 5 e^{x} x + π^{2} x^{π} + 3 π x^{π} + 2 x^{π} + π^{2} x^{π - 1} + π^{2} x^{π - 2} + π x^{π - 1} - π x^{π - 2} + 5 e^{x}

= e^{x} x^{2} + 5 e^{x} x + π^{2} x^{π} + 3 π x^{π} + 2 x^{π} + π^{2} x^{π - 1} + π^{2} x^{π - 2} + π x^{π - 1} - π x^{π - 2} + 5 e^{x}