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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

x \to 1 + lim (5 - x^{2})

\frac{d}{d x} (ln (\frac{e ^{x} + e ^{- x}}{2}))

y y^{^{'}} = - 2 x (1 + y^{2}), y (0) = 1

\int 1. 8^{0.045 \cdot x} - 1 d x

\int \frac{1}{a - b x} d x

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