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Beliebt Rechnen >

derivative f(x)=8xe^xcsc(x)

Lösung

ableitung von

f (x) = 8 x e^{x} csc (x)

Lösung

8 (e^{x} csc (x) + x (e^{x} csc (x) - e^{x} cot (x) csc (x)))

Schritte zur Lösung

\frac{d}{d x} (8 x e^{x} csc (x))

Entferne die Konstante:

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

= 8 \frac{d}{d x} (x e^{x} csc (x))

Wende die Produktregel an:

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

f = x, g = e^{x} csc (x)

= 8 (\frac{d x}{d x} e^{x} csc (x) + \frac{d}{d x} (e^{x} csc (x)) x)

\frac{d x}{d x} = 1

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

= 8 (1 \cdot e^{x} csc (x) + (e^{x} csc (x) - e^{x} cot (x) csc (x)) x)

Vereinfache

= 8 (e^{x} csc (x) + x (e^{x} csc (x) - e^{x} cot (x) csc (x)))

Graph

Beliebte Beispiele

derivative of sqrt(7)x

\frac{d}{d x} (7 x)

integral from 6 to 8 of (40)/((x-6)^3)

\int_{6}^{8} \frac{40}{( x - 6 ) ^{3}} d x

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\int \frac{1}{8 x - 1} d x

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\int sin (x^{2} - 5) d x

integral of (6x)/(x^2)

\int \frac{6 x}{x ^{2}} d x