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

The derivative of x/((x^2-1)^4) is (-7x^2-1)/((x^2-1)^5)

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

The first derivative of x/((x^2-1)^4) is (-7x^2-1)/((x^2-1)^5)

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derivative of

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

\frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

\frac{1 \cdot ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x}{( ( x ^{2} - 1 ) ^{4} ) ^{2}} : \frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

= \frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

6 x^{2} y^{2}

- 4 x^{2} cos (x)

\frac{lo g _{10} ( 1 )}{x ^{3}}

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

\frac{1}{x lo g _{10} ( x )}

What is the derivative of x/((x^2-1)^4) ?
The derivative of x/((x^2-1)^4) is (-7x^2-1)/((x^2-1)^5)
What is the first derivative of x/((x^2-1)^4) ?
The first derivative of x/((x^2-1)^4) is (-7x^2-1)/((x^2-1)^5)