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:

Read more about this topic:  Quotient Rule

Famous quotes containing the word examples:

    There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.
    Bernard Mandeville (1670–1733)

    Histories are more full of examples of the fidelity of dogs than of friends.
    Alexander Pope (1688–1744)

    It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.
    —G.C. (Georg Christoph)