d/(dt)(te^{t^3})

解答

\frac{d}{d t} (t e^{t^{3}})

e^{t^{3}} + 3 e^{t^{3}} t^{3}

求解步骤

\frac{d}{d t} (t e^{t^{3}})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = e^{t^{3}}

= \frac{d t}{d t} e^{t^{3}} + \frac{d}{d t} (e^{t^{3}}) t

\frac{d t}{d t} = 1

\frac{d}{d t} (e^{t^{3}}) = e^{t^{3}} \cdot 3 t^{2}

= 1 \cdot e^{t^{3}} + e^{t^{3}} \cdot 3 t^{2} t

化简

1 \cdot e^{t^{3}} + e^{t^{3}} \cdot 3 t^{2} t : e^{t^{3}} + 3 e^{t^{3}} t^{3}

= e^{t^{3}} + 3 e^{t^{3}} t^{3}

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