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Beliebt Rechnen >

derivative of 9x^2cos(xcot(x))

Lösung

\frac{d}{d x} (9 x^{2} cos (x) cot (x))

Lösung

9 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

Schritte zur Lösung

\frac{d}{d x} (9 x^{2} cos (x) cot (x))

Entferne die Konstante:

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

= 9 \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)

= 9 (\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)

= 9 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

Graph

Beliebte Beispiele

integral from 1 to 2 of 1/(3-x)

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

derivative of (ln(x)/(4x^2))

\frac{d}{d x} (\frac{ln ( x )}{4 x ^{2}})

integral of sqrt(x)-7cos(x)

\int x - 7 cos (x) d x

integral of sin^2((3x)/2)

\int sin^{2} (\frac{3 x}{2}) d x

derivative y= 4/(sqrt(x))

d er i v a t i v e y = \frac{4}{x}