What is the derivative of ln(x+e^x) ?

The derivative of ln(x+e^x) is (1+e^x)/(x+e^x)

What is the first derivative of ln(x+e^x) ?

The first derivative of ln(x+e^x) is (1+e^x)/(x+e^x)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{x + e ^{x}} (1 + e^{x}) : \frac{1 + e ^{x}}{x + e ^{x}}

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

y^{^{'}} = \frac{( 1 - y ) ^{5}}{4}

y = 2 x e^{- x} + 2 e^{x^{5}}

\int x^{5} - sec (x) + \frac{1}{2 x} d x

\int x I n^{2} x d x

\frac{( s + 3 )}{( s + 1 ) ( s + 2 )}

What is the derivative of ln(x+e^x) ?
The derivative of ln(x+e^x) is (1+e^x)/(x+e^x)
What is the first derivative of ln(x+e^x) ?
The first derivative of ln(x+e^x) is (1+e^x)/(x+e^x)