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Find a formula for the derivative of a given function

by RoRi

Find a formula for the derivative of the function

    \[ f(x) = \frac{x^2 + 3x + 2}{x^4 + x^2+1}. \]

Using the quotient rule for derivatives,

    \begin{align*} f'(x) &= \frac{(2x+3)(x^4 + x^2+1) - (x^2 + 3x + 2)(4x^3 + 2x)}{(x^4 + x^2 + 1)^2}\\[8pt] &= - \frac{2x^5 + 9x^4 + 8x^3 + 3x^2 + 2x - 3}{(x^4 + x^2 + 1)^2} \end{align*}

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