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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int \frac{x}{x ^{2} + 36} d x

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

2 x (\frac{d y}{d x}) - 10 y = x^{- 6}

x^{2} e^{3 x}

y^{^{''}} - 6 y^{^{'}} - 7 y = 0, y (0) = b, y^{^{'}} (0) = 8

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