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人気のある微分積分 >

derivative of e^{xi}

解

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

解

- sin (x) + i cos (x)

解答ステップ

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

簡素化

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

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

和/差の法則を適用:

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

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

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

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

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

グラフ

人気の例

integral of 3cos^2(x)sin(x)

\int 3 cos^{2} (x) sin (x) d x

integral of (2t^2+3)^{4/3}t^3

\int (2 t^{2} + 3)^{\frac{4}{3}} t^{3} d t

derivative f(x)=(x^2+3x-1)e^x

d er i v a t i v e f (x) = (x^{2} + 3 x - 1) e^{x}

limit as n approaches infinity of |((2n)^{2n})/((2n+2)^{2n)}|

n \to \infty lim (\frac{( 2 n ) ^{2 n}}{( 2 n + 2 ) ^{2 n}})

limit as x approaches 2 of 3x-1

x \to 2 lim (3 x - 1)