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Beliebt Rechnen >

derivative of 7x^2sin(xtan(x))

Lösung

\frac{d}{d x} (7 x^{2} sin (x) tan (x))

Lösung

7 (2 x sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{2})

Schritte zur Lösung

\frac{d}{d x} (7 x^{2} sin (x) tan (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (x^{2} sin (x) tan (x))

Wende die Produktregel an:

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

f = x^{2}, g = sin (x) tan (x)

= 7 (\frac{d}{d x} (x^{2}) sin (x) tan (x) + \frac{d}{d x} (sin (x) tan (x)) x^{2})

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

\frac{d}{d x} (sin (x) tan (x)) = sin (x) (1 + sec^{2} (x))

= 7 (2 x sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{2})

Graph

Beliebte Beispiele

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integral of 1/(tan(v))

\int \frac{1}{tan ( v )} d v

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\int_{0}^{8} \frac{1}{8 - x} d x

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d er i v a t i v e x^{2} arctan (3 x)

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