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Beliebt Rechnen >

derivative f(x)=sin^4(sqrt(x))

Lösung

ableitung von

f (x) = sin^{4} (x)

Lösung

\frac{2 sin ^{3} ( x ) cos ( x )}{x}

Schritte zur Lösung

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

Wende die Kettenregel an:

4 (sin (x))^{3} \frac{d}{d x} (sin (x))

= 4 (sin (x))^{3} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = \frac{cos ( x )}{2 x}

= 4 (sin (x))^{3} \frac{cos ( x )}{2 x}

Vereinfache

4 sin^{3} (x) \frac{cos ( x )}{2 x} : \frac{2 sin ^{3} ( x ) cos ( x )}{x}

= \frac{2 sin ^{3} ( x ) cos ( x )}{x}

Graph

Beliebte Beispiele

integral of 1/((x^2-x-2)(x-2))

\int \frac{1}{( x ^{2} - x - 2 ) ( x - 2 )} d x

y^{^{'}} = 2 y - y^{2}

integral of sqrt(2px)

\int 2 p x d x

derivative of (cos(2x)^x)

\frac{d}{d x} ((cos (2 x))^{x})

integral from 1 to infinity of 2e^{-2x}

\int_{1}^{\infty} 2 e^{- 2 x} d x