What is the derivative of (x^2-10x+2/(x(x^2-1))) ?

The derivative of (x^2-10x+2/(x(x^2-1))) is (-x^4+20x^3-7x^2+2)/(x^2(x^2-1)^2)

What is the first derivative of (x^2-10x+2/(x(x^2-1))) ?

The first derivative of (x^2-10x+2/(x(x^2-1))) is (-x^4+20x^3-7x^2+2)/(x^2(x^2-1)^2)

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\frac{d}{d x} (\frac{x ^{2} - 10 x + 2}{x ( x ^{2} - 1 )})

\frac{- x ^{4} + 20 x ^{3} - 7 x ^{2} + 2}{x ^{2} ( x ^{2} - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 10 x + 2}{x ( x ^{2} - 1 )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 10 x + 2 ) x ( x ^{2} - 1 ) - \frac{d}{d x} ( x ( x ^{2} - 1 ) ) ( x ^{2} - 10 x + 2 )}{( x ( x ^{2} - 1 ) ) ^{2}}

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

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

= \frac{( 2 x - 10 ) x ( x ^{2} - 1 ) - ( 3 x ^{2} - 1 ) ( x ^{2} - 10 x + 2 )}{( x ( x ^{2} - 1 ) ) ^{2}}

Simplify

\frac{( 2 x - 10 ) x ( x ^{2} - 1 ) - ( 3 x ^{2} - 1 ) ( x ^{2} - 10 x + 2 )}{( x ( x ^{2} - 1 ) ) ^{2}} : \frac{- x ^{4} + 20 x ^{3} - 7 x ^{2} + 2}{x ^{2} ( x ^{2} - 1 ) ^{2}}

= \frac{- x ^{4} + 20 x ^{3} - 7 x ^{2} + 2}{x ^{2} ( x ^{2} - 1 ) ^{2}}

What is the derivative of (x^2-10x+2/(x(x^2-1))) ?
The derivative of (x^2-10x+2/(x(x^2-1))) is (-x^4+20x^3-7x^2+2)/(x^2(x^2-1)^2)
What is the first derivative of (x^2-10x+2/(x(x^2-1))) ?
The first derivative of (x^2-10x+2/(x(x^2-1))) is (-x^4+20x^3-7x^2+2)/(x^2(x^2-1)^2)