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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int x^{5} e^{3 x} d x

f (x) = (x + 3)^{2}

\int_{\frac{1}{2}}^{1} (x^{- 3} - 2) d x

y = 6 x e^{x}, (0, 0)

cos (4 t)

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