What is the derivative of (x^2/((x^2-1)^4)) ?

The derivative of (x^2/((x^2-1)^4)) is (2x(-3x^2-1))/((x^2-1)^5)

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

The first derivative of (x^2/((x^2-1)^4)) is (2x(-3x^2-1))/((x^2-1)^5)

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

\frac{2 x ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{5}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((x^{2} - 1)^{4}) = 8 x (x^{2} - 1)^{3}

= \frac{2 x ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x ^{2}}{( ( x ^{2} - 1 ) ^{4} ) ^{2}}

Simplify

\frac{2 x ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x ^{2}}{( ( x ^{2} - 1 ) ^{4} ) ^{2}} : \frac{2 x ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{5}}

= \frac{2 x ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{5}}

What is the derivative of (x^2/((x^2-1)^4)) ?
The derivative of (x^2/((x^2-1)^4)) is (2x(-3x^2-1))/((x^2-1)^5)
What is the first derivative of (x^2/((x^2-1)^4)) ?
The first derivative of (x^2/((x^2-1)^4)) is (2x(-3x^2-1))/((x^2-1)^5)