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

Name: Problem 16, Chapter 4: Calculus with Applications
Uploaded: 2019-04-07T01:36:11-08:00
Duration: 3 min 8 s
Channel: Smita Praharaj
Description: Use the quotient rule to find the derivative of the following. y=(x^2-4 x)/(x+3)

step 1 In this problem, we are asked to find the derivative of the function, y equals x squared minus 4

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

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Key Concepts

Algebraic Simplification

After applying differentiation rules such as the quotient rule, simplifying the resulting expression is important. This involves factoring, combining like terms, and reducing fractions to present the derivative in its simplest and most understandable form.

Polynomial Differentiation

Polynomial differentiation involves applying the power rule to each term of a polynomial function. This process is particularly useful when the numerator or denominator of a quotient is a polynomial, simplifying the calculation of derivatives before or after applying the quotient rule.

Derivative

The derivative measures the rate at which a function changes with respect to a change in its input variable. It is a fundamental concept in calculus used to analyze the behavior of functions and to find slopes of tangent lines to the curve at given points.

Quotient Rule

The quotient rule is a method of differentiating functions that are expressed as the ratio of two differentiable functions. It states that if a function is given by the quotient f(x)/g(x), then its derivative is (f'(x)g(x) - f(x)g'(x)) divided by [g(x)]², which is essential for handling fractions in differentiation.

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