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Popular >

derivative of f(x)=ln(sqrt(x(1-x)))

Solution

derivative of

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

Solution

\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 )}

Popular Examples

integral from 1 to 6 of 1/x

\int_{1}^{6} \frac{1}{x} d x

integral of 1/(x(x^4-1))

\int \frac{1}{x ( x ^{4} - 1 )} d x

(2xy-9x^2)dx+(2y+x^2+1)dy=0

(2 x y - 9 x^{2}) d x + (2 y + x^{2} + 1) d y = 0

integral of (4x)/(x^2+2x-3)

\int \frac{4 x}{x ^{2} + 2 x - 3} d x

tangent of f(x)=tan(x),\at x=0 tangent of

f (x) = tan (x), at x = 0

Frequently Asked Questions (FAQ)

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))