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Beliebt Rechnen >

derivative of (x^3/(cos(x)))

Lösung

\frac{d}{d x} (\frac{x ^{3}}{cos ( x )})

Lösung

3 x^{2} sec (x) + sec (x) tan (x) x^{3}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3}}{cos ( x )})

Vereinfache

\frac{x ^{3}}{cos ( x )} : x^{3} sec (x)

= \frac{d}{d x} (x^{3} sec (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = sec (x)

= \frac{d}{d x} (x^{3}) sec (x) + \frac{d}{d x} (sec (x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= 3 x^{2} sec (x) + sec (x) tan (x) x^{3}

Graph

Beliebte Beispiele

derivative 2-3x

d er i v a t i v e 2 - 3 x

integral of 4-y^2

\int 4 - y^{2} d y

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\int x^{5} \cdot e^{x} d x

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\int \frac{t + 1}{t} d t