Question

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find the derivative of the function.
f(x) = (x + 1)/(4x^2 + 6x + 7)
f(x) =
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Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $f(x)=\frac{u(x)}{v(x)}$, then $f^{\prime}(x)=\frac{u^{\prime}(x)v(x)-u(x)v^{\prime}(x)}{v(x)^2}$. Here, $u(x)=x + 1$, so $u^{\prime}(x)=1$, and $v(x)=4x^{2}+6x + 7$, so $v^{\prime}(x)=8x+6$.

Step2: Substitute into quotient - rule

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Answer:

$\frac{-4x^{2}-8x + 1}{(4x^{2}+6x + 7)^{2}}$