What is the derivative of 1/((x^2-1)(x^2+5x+5)) ?

The derivative of 1/((x^2-1)(x^2+5x+5)) is -(4x^3+15x^2+8x-5)/((x^2-1)^2(x^2+5x+5)^2)

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

The first derivative of 1/((x^2-1)(x^2+5x+5)) is -(4x^3+15x^2+8x-5)/((x^2-1)^2(x^2+5x+5)^2)

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derivative of

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

- \frac{4 x ^{3} + 15 x ^{2} + 8 x - 5}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 5 x + 5 ) ^{2}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{2} - 1) (x^{2} + 5 x + 5)) = 4 x^{3} + 15 x^{2} + 8 x - 5

= - \frac{1}{( ( x ^{2} - 1 ) ( x ^{2} + 5 x + 5 ) ) ^{2}} (4 x^{3} + 15 x^{2} + 8 x - 5)

Simplify

- \frac{1}{( ( x ^{2} - 1 ) ( x ^{2} + 5 x + 5 ) ) ^{2}} (4 x^{3} + 15 x^{2} + 8 x - 5) : - \frac{4 x ^{3} + 15 x ^{2} + 8 x - 5}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 5 x + 5 ) ^{2}}

= - \frac{4 x ^{3} + 15 x ^{2} + 8 x - 5}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 5 x + 5 ) ^{2}}

What is the derivative of 1/((x^2-1)(x^2+5x+5)) ?
The derivative of 1/((x^2-1)(x^2+5x+5)) is -(4x^3+15x^2+8x-5)/((x^2-1)^2(x^2+5x+5)^2)
What is the first derivative of 1/((x^2-1)(x^2+5x+5)) ?
The first derivative of 1/((x^2-1)(x^2+5x+5)) is -(4x^3+15x^2+8x-5)/((x^2-1)^2(x^2+5x+5)^2)