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

The derivative of ((x+2)/((x-1))) is -3/((x-1)^2)

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

The first derivative of ((x+2)/((x-1))) is -3/((x-1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x^{12}

\int sin^{4} (5 x) cos^{6} (5 x) d x

\frac{d}{d x} (- 5 x^{- 6})

\int 11 tan^{3} (x) sec (x) d x

\frac{d}{d x} ((sin (5 x))^{l n (x)})

What is the derivative of ((x+2)/((x-1))) ?
The derivative of ((x+2)/((x-1))) is -3/((x-1)^2)
What is the first derivative of ((x+2)/((x-1))) ?
The first derivative of ((x+2)/((x-1))) is -3/((x-1)^2)