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Beliebt Rechnen >

derivative of ln(1+e^{2x})

Lösung

\frac{d}{d x} (ln (1 + e^{2 x}))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (ln (1 + e^{2 x}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{1 + e ^{2 x}} \cdot 2 e^{2 x} : \frac{2 e ^{2 x}}{1 + e ^{2 x}}

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

Graph

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(\partial)/(\partial x)(-3y^3+3x^2y^2-y)

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