What is the derivative of ln(1+x-x) ?

The derivative of ln(1+x-x) is 1/(1+x)-1

What is the first derivative of ln(1+x-x) ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d x}{d x} = 1

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

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