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Beliebt Rechnen >

derivative 6x^2cos(x)cot(x)

Lösung

ableitung von

6 x^{2} cos (x) cot (x)

Lösung

6 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

Schritte zur Lösung

\frac{d}{d x} (6 x^{2} cos (x) cot (x))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{2} cos (x) cot (x))

Wende die Produktregel an:

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

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

= 6 (\frac{d}{d x} (x^{2}) cos (x) cot (x) + \frac{d}{d x} (cos (x) cot (x)) x^{2})

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

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

= 6 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

Graph

Beliebte Beispiele

integral from 1 to 3 of x^3+2x-3

\int_{1}^{3} x^{3} + 2 x - 3 d x

derivative f(x)=(3x+5)^2

d er i v a t i v e f (x) = (3 x + 5)^{2}

integral of 1/(cos(x)+1)

\int \frac{1}{cos ( x ) + 1} d x

derivative f(x)=3x^2+2x+1

d er i v a t i v e f (x) = 3 x^{2} + 2 x + 1

fläche x^2-4x+7,2x^2-3x+1

a re a x^{2} - 4 x + 7, 2 x^{2} - 3 x + 1