d/(dt)(e^{it})

解答

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

- sin (t) + i cos (t)

求解步骤

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

化简

e^{i t} : cos (t) + i sin (t)

= \frac{d}{d t} (cos (t) + i sin (t))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (cos (t)) + \frac{d}{d t} (i sin (t))

\frac{d}{d t} (cos (t)) = - sin (t)

\frac{d}{d t} (i sin (t)) = i cos (t)

= - sin (t) + i cos (t)

\frac{d x}{d t} = sin (2 π (t + 3))

in v erse l a pl a ce 1

\int (517 - \frac{x ^{3}}{7})^{5} x^{2} d x

n = 3 \sum \infty \frac{1}{3} (\frac{2}{5})^{n}

\int \frac{1}{5 ^{4 x}} d x