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

The derivative of ln(xsqrt(2-x)) is (-3x+4)/(2x(2-x))

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

The first derivative of ln(xsqrt(2-x)) is (-3x+4)/(2x(2-x))

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derivative of

ln (x 2 - x)

\frac{- 3 x + 4}{2 x ( 2 - x )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x 2 - x) = \frac{- 3 x + 4}{2 2 - x}

= \frac{1}{x 2 - x} \cdot \frac{- 3 x + 4}{2 2 - x}

Simplify

\frac{1}{x 2 - x} \cdot \frac{- 3 x + 4}{2 2 - x} : \frac{- 3 x + 4}{2 x ( 2 - x )}

= \frac{- 3 x + 4}{2 x ( 2 - x )}

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (3 t)

\frac{d}{d x} (- cos (π x))

t^{2} y^{^{'}} + 4 t y - y^{3} = 0

x^{2}, 9 + x

\int csc^{2} (t) - 2 e^{t} d t

What is the derivative of ln(xsqrt(2-x)) ?
The derivative of ln(xsqrt(2-x)) is (-3x+4)/(2x(2-x))
What is the first derivative of ln(xsqrt(2-x)) ?
The first derivative of ln(xsqrt(2-x)) is (-3x+4)/(2x(2-x))