What is (\partial)/(\partial x)(ln(1+x)) ?

The answer to (\partial)/(\partial x)(ln(1+x)) is 1/(1+x)

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(\partial)/(\partial x)(ln(1+x))

\frac{\partial}{\partial x} (ln (1 + x))

\frac{1}{1 + x}

Solution steps

\frac{\partial}{\partial x} (ln (1 + x))

Apply the chain rule:

\frac{1}{1 + x} \frac{\partial}{\partial x} (1 + x)

= \frac{1}{1 + x} \frac{\partial}{\partial x} (1 + x)

\frac{\partial}{\partial x} (1 + x) = 1

= \frac{1}{1 + x} \cdot 1

Simplify

= \frac{1}{1 + x}

\int_{0}^{10} 20 x e^{- 0.6 x} d x

\int \frac{x + 2}{x} d x

x \to 0 lim (\frac{3 ^{x} - 2 ^{x}}{x})

\frac{\partial}{\partial x} (\frac{x}{x + 3})

f (x) = \frac{x}{x ^{2} - 1}

What is (\partial)/(\partial x)(ln(1+x)) ?
The answer to (\partial)/(\partial x)(ln(1+x)) is 1/(1+x)