What is the derivative of ln(sqrt(2-x)) ?

The derivative of ln(sqrt(2-x)) is -1/(2(2-x))

What is the first derivative of ln(sqrt(2-x)) ?

The first derivative of ln(sqrt(2-x)) is -1/(2(2-x))

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derivative of

ln (2 - x)

- \frac{1}{2 ( 2 - x )}

Solution steps

\frac{d}{d x} (ln (2 - x))

Apply the chain rule:

\frac{1}{2 - x} \frac{d}{d x} (2 - x)

= \frac{1}{2 - x} \frac{d}{d x} (2 - x)

\frac{d}{d x} (2 - x) = - \frac{1}{2 2 - x}

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

Simplify

\frac{1}{2 - x} (- \frac{1}{2 2 - x}) : - \frac{1}{2 ( 2 - x )}

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

What is the derivative of ln(sqrt(2-x)) ?
The derivative of ln(sqrt(2-x)) is -1/(2(2-x))
What is the first derivative of ln(sqrt(2-x)) ?
The first derivative of ln(sqrt(2-x)) is -1/(2(2-x))