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Beliebt Rechnen >

derivative of sin^n(x)

Lösung

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

Lösung

n cos (x) sin^{n - 1} (x)

Schritte zur Lösung

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

Wende die Kettenregel an:

n (sin (x))^{n - 1} \frac{d}{d x} (sin (x))

= n (sin (x))^{n - 1} \frac{d}{d x} (sin (x))

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

= n (sin (x))^{n - 1} cos (x)

Vereinfache

= n cos (x) sin^{n - 1} (x)

Graph

Beliebte Beispiele

4xy^3y^'=x^4+4y^4

4 x y^{3} y^{^{'}} = x^{4} + 4 y^{4}

integral of sqrt(49-x^2)

\int 49 - x^{2} d x

integral of (x^5-x^3+8x)/(x^4)

\int \frac{x ^{5} - x ^{3} + 8 x}{x ^{4}} d x

derivative of (1+x^{3/2})

\frac{d}{d x} ((1 + x)^{\frac{3}{2}})

limit as x approaches 2-of 10-x-x^2

x \to 2 - lim (10 - x - x^{2})