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

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

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

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

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derivative of

ln (1 - x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{- 5}^{0} (2 + 25 - x^{2}) d x

x^{2} y^{^{'}} + (2 x^{2} - x) y = x^{4}

\frac{\partial}{\partial y} (x^{2} - \frac{y}{4})

9

f (x) = \frac{8 x}{x ^{2} + 1}, at x = 0

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