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Beliebt Rechnen >

derivative of 5x^2cos(xcot(x))

Lösung

\frac{d}{d x} (5 x^{2} cos (x) cot (x))

Lösung

5 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

Schritte zur Lösung

\frac{d}{d x} (5 x^{2} cos (x) cot (x))

Entferne die Konstante:

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

= 5 \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)

= 5 (\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)

= 5 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

Graph

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laplacetransform 3e^{-t}

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limit as s approaches 2/3 of 3s(2s-1)

s \to \frac{2}{3} lim (3 s (2 s - 1))

integral of 9/(64+4r^2)

\int \frac{9}{64 + 4 r ^{2}} d r

derivative of 9x^3-7x

\frac{d}{d x} (9 x^{3} - 7 x)

derivative of (x^3+3^5)

\frac{d}{d x} ((x^{3} + 3)^{5})