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Beliebt Rechnen >

(\partial)/(\partial x)(e^{ix})

Lösung

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

Lösung

- sin (x) + i cos (x)

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Beliebte Beispiele

y^{^{'}} + y = t

derivative of (sqrt(x)/(x+3))

\frac{d}{d x} (\frac{x}{x + 3})

integral of 1/(x^2sqrt(9+x^2))

\int \frac{1}{x ^{2} 9 + x ^{2}} d x

(dy)/(dx)=e^{-x^2},y(3)=5

\frac{d y}{d x} = e^{- x^{2}}, y (3) = 5

integral of (4-3x)^5+e^{2x+5}+sin(9x)

\int (4 - 3 x)^{5} + e^{2 x + 5} + sin (9 x) d x