derivative 7e^xarctan(x)

Lösung

ableitung von

7 e^{x} arctan (x)

7 (e^{x} arctan (x) + \frac{e ^{x}}{x ^{2} + 1})

Schritte zur Lösung

\frac{d}{d x} (7 e^{x} arctan (x))

Entferne die Konstante:

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

= 7 \frac{d}{d x} (e^{x} arctan (x))

Wende die Produktregel an:

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

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

= 7 (\frac{d}{d x} (e^{x}) arctan (x) + \frac{d}{d x} (arctan (x)) e^{x})

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

\frac{d}{d x} (arctan (x)) = \frac{1}{x ^{2} + 1}

= 7 (e^{x} arctan (x) + \frac{1}{x ^{2} + 1} e^{x})

\frac{1}{x ^{2} + 1} e^{x} = \frac{e ^{x}}{x ^{2} + 1}

= 7 (e^{x} arctan (x) + \frac{e ^{x}}{x ^{2} + 1})

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