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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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