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

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

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

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

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derivative of

f (x) = ln (x (1 - x))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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