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

The derivative of y= 1/((x^2-2)(x^2+x+5)) is -(4x^3+3x^2+6x-2)/((x^2-2)^2(x^2+x+5)^2)

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

The first derivative of y= 1/((x^2-2)(x^2+x+5)) is -(4x^3+3x^2+6x-2)/((x^2-2)^2(x^2+x+5)^2)

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derivative of

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

- \frac{4 x ^{3} + 3 x ^{2} + 6 x - 2}{( x ^{2} - 2 ) ^{2} ( x ^{2} + x + 5 ) ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{2} - 2) (x^{2} + x + 5)) = 4 x^{3} + 3 x^{2} + 6 x - 2

= - \frac{1}{( ( x ^{2} - 2 ) ( x ^{2} + x + 5 ) ) ^{2}} (4 x^{3} + 3 x^{2} + 6 x - 2)

Simplify

- \frac{1}{( ( x ^{2} - 2 ) ( x ^{2} + x + 5 ) ) ^{2}} (4 x^{3} + 3 x^{2} + 6 x - 2) : - \frac{4 x ^{3} + 3 x ^{2} + 6 x - 2}{( x ^{2} - 2 ) ^{2} ( x ^{2} + x + 5 ) ^{2}}

= - \frac{4 x ^{3} + 3 x ^{2} + 6 x - 2}{( x ^{2} - 2 ) ^{2} ( x ^{2} + x + 5 ) ^{2}}

y = 5 x cos (x), (π, - 5 π)

y = csc^{3} (2 x)

\frac{d}{d x} ((a x + b) e^{- x})

\int [x (x^{2} - 1) + csc^{2} (x)] d x

4 sin (x) sin (x)

What is the derivative of y= 1/((x^2-2)(x^2+x+5)) ?
The derivative of y= 1/((x^2-2)(x^2+x+5)) is -(4x^3+3x^2+6x-2)/((x^2-2)^2(x^2+x+5)^2)
What is the first derivative of y= 1/((x^2-2)(x^2+x+5)) ?
The first derivative of y= 1/((x^2-2)(x^2+x+5)) is -(4x^3+3x^2+6x-2)/((x^2-2)^2(x^2+x+5)^2)