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Beliebt Rechnen >

derivative of x^3cot(x)

Lösung

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

Lösung

3 x^{2} cot (x) - x^{3} csc^{2} (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= 3 x^{2} cot (x) + (- csc^{2} (x)) x^{3}

Vereinfache

= 3 x^{2} cot (x) - x^{3} csc^{2} (x)

Graph

Beliebte Beispiele

integral of ((sin(sqrt(w))))/(sqrt(w))

\int \frac{( sin ( w ) )}{w} d w

inverselaplace ((s-2))/((s-2)^2-3)

in v erse l a pl a ce \frac{( s - 2 )}{( s - 2 ) ^{2} - 3}

integral of ((e^x))/(1+e^x)

\int \frac{( e ^{x} )}{1 + e ^{x}} d x

derivative y=4tsqrt(t+7)

d er i v a t i v e y = 4 t t + 7

integral from-2 to 2 of x^2-1

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