derivative e^tsin(6t)

解答

导数

e^{t} sin (6 t)

e^{t} sin (6 t) + cos (6 t) \cdot 6 e^{t}

求解步骤

\frac{d}{d t} (e^{t} sin (6 t))

使用微分乘法定则:

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

f = e^{t}, g = sin (6 t)

= \frac{d}{d t} (e^{t}) sin (6 t) + \frac{d}{d t} (sin (6 t)) e^{t}

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

\frac{d}{d t} (sin (6 t)) = cos (6 t) \cdot 6

= e^{t} sin (6 t) + cos (6 t) \cdot 6 e^{t}

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