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Beliebt Rechnen >

d/(dn)(e^{nipi})

Lösung

\frac{d}{d n} (e^{niπ})

Lösung

- sin (πn) π + i cos (πn) π

Schritte zur Lösung

\frac{d}{d n} (e^{niπ})

Vereinfache

e^{niπ} : cos (πn) + i sin (πn)

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d n} (cos (πn)) = - sin (πn) π

\frac{d}{d n} (i sin (πn)) = i cos (πn) π

= - sin (πn) π + i cos (πn) π

Graph

Beliebte Beispiele

y^{^{''}} + y^{^{'}} + y = 0

integral of (y^5+5y)

\int (y^{5} + 5 y) d y

y^{''}+y=0,y(pi/3)=16,y^'(pi/3)=-32

y^{^{''}} + y = 0, y (\frac{π}{3}) = 16, y^{^{'}} (\frac{π}{3}) = - 32

(\partial)/(\partial y)(7e^{x^2ln(y)})

\frac{\partial}{\partial y} (7 e^{x^{2} l n (y)})

derivative 5Y^{5/8}X^{3/8}

d er i v a t i v e 5 Y^{\frac{5}{8}} X^{\frac{3}{8}}