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

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

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

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

1 - \frac{1}{x + 1}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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