Find the derivative of each function. f(x)=(x)/(x^2-4)-(x-1)/(x^2+4)

Name: Problem 29, Chapter 3: Applied Calculus for the Managerial, Life, and Social Sciences
Uploaded: 2021-05-06T15:23:13-08:00
Duration: 5 min 14 s
Channel: Naresh Bagrecha
Description: Find the derivative of each function. f(x)=(x)/(x^2-4)-(x-1)/(x^2+4)

step 1 In the Qion given function is fx is equal to x divided by x squared minus 4 minus x minus 1 divi

Find the derivative of each function....

Key Concepts

Algebraic Simplification

After applying differentiation techniques such as the quotient rule, the resulting expressions often require algebraic simplification. This involves combining like terms, factoring common factors, and reducing fractions to express the derivative in its simplest and most interpretable form.

Differentiation

Differentiation is the process of computing the derivative of a function, which measures the rate at which the function's value changes with respect to changes in its input. It is a fundamental concept in calculus and provides the basis for analyzing rates of change in various mathematical, physical, and economic contexts.

Quotient Rule

The quotient rule is a differentiation method used when a function is expressed as the quotient of two differentiable functions. It states that the derivative of a function h(x) = f(x)/g(x) is given by h'(x) = (g(x)f'(x) - f(x)g'(x)) / [g(x)]². This rule is essential when handling rational functions where both numerator and denominator are functions of x.

Linearity of Differentiation

Linearity in differentiation means that the derivative of a sum or difference of functions equals the sum or difference of their derivatives. This property allows one to differentiate complex expressions by applying the derivative operator to each term individually, making the overall process more systematic.

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