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Beliebt Rechnen >

derivative of xsin(xtan(x))

Lösung

\frac{d}{d x} (x sin (x) tan (x))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (x sin (x) tan (x))

Wende die Produktregel an:

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

f = x, g = sin (x) tan (x)

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

Graph

Beliebte Beispiele

derivative of (x^{3/2}-4x(x^4-3/(x^2)+2))

derivative sqrt(4x+2)

derivative of (2x^2+5x+8/(2x^2))

derivative f(x)=3e^x

inverselaplace 1/(s^2+8s+16)