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Beliebt Rechnen >

derivative of 11x^2cot(x)

Lösung

\frac{d}{d x} (11 x^{2} cot (x))

Lösung

11 (2 x cot (x) - x^{2} csc^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (11 x^{2} cot (x))

Entferne die Konstante:

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

= 11 \frac{d}{d x} (x^{2} cot (x))

Wende die Produktregel an:

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

f = x^{2}, g = cot (x)

= 11 (\frac{d}{d x} (x^{2}) cot (x) + \frac{d}{d x} (cot (x)) x^{2})

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

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

= 11 (2 x cot (x) + (- csc^{2} (x)) x^{2})

Vereinfache

= 11 (2 x cot (x) - x^{2} csc^{2} (x))

Graph

Beliebte Beispiele

f (x) = 4

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\int cos (v) sin (v) d v

(\partial)/(\partial x)(cos(6y-x))

\frac{\partial}{\partial x} (cos (6 y - x))

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a re a 20 + x - x^{2}, x^{2} - 5 x

d er i v a t i v e 7^{x}