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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((x - 1)^{2} (x + 1)^{2}) = 4 x^{3} - 4 x

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

Simplify

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

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

x = (y - 1)^{2}, x = 13 - y^{2}

\int \frac{2 x}{e ^{2 x}} d x

x \to 2 + lim (g (x))

\frac{d}{d x} (arctan (8^{x}))

\int - 0.006 t^{2} + 0.2 t d t

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