(d^3)/(dx^3)(x^6e^x)

解答

\frac{d ^{3}}{d x ^{3}} (x^{6} e^{x})

e^{x} x^{6} + 18 e^{x} x^{5} + 90 e^{x} x^{4} + 120 e^{x} x^{3}

求解步骤

\frac{d ^{3}}{d x ^{3}} (x^{6} e^{x})

\frac{d}{d x} (x^{6} e^{x}) = 6 x^{5} e^{x} + e^{x} x^{6}

= \frac{d ^{2}}{d x ^{2}} (6 x^{5} e^{x} + e^{x} x^{6})

\frac{d}{d x} (6 x^{5} e^{x} + e^{x} x^{6}) = e^{x} x^{6} + 12 e^{x} x^{5} + 30 e^{x} x^{4}

= \frac{d}{d x} (e^{x} x^{6} + 12 e^{x} x^{5} + 30 e^{x} x^{4})

\frac{d}{d x} (e^{x} x^{6} + 12 e^{x} x^{5} + 30 e^{x} x^{4}) = e^{x} x^{6} + 18 e^{x} x^{5} + 90 e^{x} x^{4} + 120 e^{x} x^{3}

= e^{x} x^{6} + 18 e^{x} x^{5} + 90 e^{x} x^{4} + 120 e^{x} x^{3}

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