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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = \frac{( 1 + x )}{x y ^{16}}

\int (2 x - 40) \cdot ln (x - 20) d x

\int_{0}^{1} (u + 3) (u - 4) d u

f (x) = 3 x^{\frac{5}{4}}

csc (x)

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