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Beliebt Rechnen >

derivative f(x)=sin^5(x)

Lösung

ableitung von

f (x) = sin^{5} (x)

Lösung

5 sin^{4} (x) cos (x)

Schritte zur Lösung

\frac{d}{d x} (sin^{5} (x))

Wende die Kettenregel an:

5 (sin (x))^{4} \frac{d}{d x} (sin (x))

= 5 (sin (x))^{4} \frac{d}{d x} (sin (x))

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

= 5 (sin (x))^{4} cos (x)

Vereinfache

= 5 sin^{4} (x) cos (x)

Graph

Beliebte Beispiele

d/(dt)(arcsin(sqrt(2t)))

\frac{d}{d t} (arcsin (2 t))

derivative of (x^4/5)

\frac{d}{d x} (\frac{x ^{4}}{5})

tangent f(x)=-x^3-3x^2-3,\at x=-3

t an g e n t f (x) = - x^{3} - 3 x^{2} - 3, at x = - 3

limit as x approaches-1 of (x+2)/(x^2+x)

x \to - 1 lim (\frac{x + 2}{x ^{2} + x})

integral of sqrt(1/x)

\int \frac{1}{x} d x