Use the quotient rule to find the derivative of the following. f(x)=((3 x^2+1)(2 x-1))/(5 x+4)

Name: Problem 27, Chapter 12: Finite Mathematics and Calculus with Applications
Uploaded: 2020-05-03T02:05:48-08:00
Duration: 4 min 14 s
Channel: Amy Jiang
Description: Use the quotient rule to find the derivative of the following. f(x)=((3 x^2+1)(2 x-1))/(5 x+4)

step 1 Okay, so before we use our quotient rule, to find the derivative. I'm going to start by multiply

Use the quotient rule to find the derivative of the...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Quotient Rule

The quotient rule is a method used to differentiate a function expressed as the division of two differentiable functions. It states that if a function is written as f(x) = g(x)/h(x), then its derivative is given by (h(x)g'(x) - g(x)h'(x))/(h(x))^2. This rule is essential for finding derivatives of rational functions.

Product Rule

The product rule is applied when differentiating products of differentiable functions. It states that if u(x) and v(x) are functions, then the derivative of their product is u'(x)v(x) + u(x)v'(x). This rule is important when the numerator of a rational function, for instance, is itself a product of two or more functions.

Polynomial Differentiation

Polynomial differentiation involves applying fundamental derivative rules, such as the power rule and constant multiple rule, to each term in a polynomial function. These techniques are used to compute the necessary derivatives in both the numerator and the denominator of a rational function when applying the quotient rule.

Transcript

Please give Ace some feedback