Quotient Rule - Examples

Examples

The derivative of is:

$\begin{align}\frac{d}{dx}\left &= \frac{(x^2 + 1)(4) - (4x - 2)(2x)}{(x^2 + 1)^2}\\ & = \frac{(4x^2 + 4) - (8x^2 - 4x)}{(x^2 + 1)^2} = \frac{-4x^2 + 4x + 4}{(x^2 + 1)^2}\end{align}$

In the example above, the choices

were made. Analogously, the derivative of sin(x)/x2 (when x ≠ 0) is:

Another example is:

whereas and, and and .

The derivative of is determined as follows:

This can be checked by using laws of exponents and the power rule:

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