Find the derivative of the function.
{eq}h(x) = \frac{4x^{3} \space + \space 2x \space + \space 5}{x} {/eq}
Question:
Find the derivative of the function.
{eq}h(x) = \frac{4x^{3} \space + \space 2x \space + \space 5}{x} {/eq}
Derivative of function using quotient rule
The quotient rule of differentiation states that if, given two functions, in the form below, the derivative of the function will be:
{eq}\begin{align*} &y = \dfrac{{f\left( x \right)}}{{g\left( x \right)}}\\ &y' = \dfrac{{f'\left( x \right)g\left( x \right) - g'\left( x \right)f\left( x \right).}}{{{g^2}\left( x \right)}} \end{align*} {/eq}
Some standard formulae used in the differentiation of function are:
{eq}\dfrac{d}{{dx}}\left( {{x^n}} \right) = n{x^{n - 1}}. {/eq}
Answer and Explanation: 1
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View this answerGiven the function, we can specify the functions {eq}f(x) {/eq} and {eq}g(x) {/eq} according to the definition above as:
{eq}\begin{align*} &f\lef...
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Chapter 8 / Lesson 8The quotient rule can be used for differentiation when taking the derivative of a function divided by another function. Gain a better understanding of when to use the quotient rule and explore some examples in this lesson.