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

The derivative of (-(x+1)/((x-1)^3)) is (2(x+2))/((x-1)^4)

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

The first derivative of (-(x+1)/((x-1)^3)) is (2(x+2))/((x-1)^4)

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

\frac{2 ( x + 2 )}{( x - 1 ) ^{4}}

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{2 ( x + 2 )}{( x - 1 ) ^{4}}

\int cos^{4} (7 x + 3) d x

\frac{d y}{d x} = 4 y + a

t^{2} e^{- 4 t}

x^{5}

sin (π \cdot x)

What is the derivative of (-(x+1)/((x-1)^3)) ?
The derivative of (-(x+1)/((x-1)^3)) is (2(x+2))/((x-1)^4)
What is the first derivative of (-(x+1)/((x-1)^3)) ?
The first derivative of (-(x+1)/((x-1)^3)) is (2(x+2))/((x-1)^4)