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:

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

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)

    “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)