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Beliebt Rechnen >

derivative of (0.9e^x/(tan(x)))

Lösung

\frac{d}{d x} (\frac{0.9 e ^{x}}{tan ( x )})

Lösung

0.9 (e^{x} cot (x) - e^{x} csc^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (\frac{0.9 e ^{x}}{tan ( x )})

Vereinfache

\frac{0.9 e ^{x}}{tan ( x )} : 0.9 e^{x} cot (x)

= \frac{d}{d x} (0.9 e^{x} cot (x))

Entferne die Konstante:

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

= 0.9 \frac{d}{d x} (e^{x} cot (x))

Wende die Produktregel an:

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

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

= 0.9 (\frac{d}{d x} (e^{x}) cot (x) + \frac{d}{d x} (cot (x)) e^{x})

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

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

= 0.9 (e^{x} cot (x) + (- csc^{2} (x)) e^{x})

Vereinfache

= 0.9 (e^{x} cot (x) - e^{x} csc^{2} (x))

Graph

Beliebte Beispiele

(x^{\frac{1}{3}})^{^{'}}

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\int_{0}^{\infty} 77 \frac{e ^{x}}{e ^{2 x} + 3} d x

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\int_{- 4}^{4} (16 - x^{2}) d x