Find f^'(x). f(x)=-2 lnx+x^2-4

Name: Problem 11, Chapter 3: Calculus for Business, Economics, Life Sciences, and Social Sciences
Uploaded: 2021-02-22T17:18:17-08:00
Duration: 1 min 21 s
Channel: Gregory Higby
Description: Find f^'(x). f(x)=-2 lnx+x^2-4

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Key Concepts

Differentiation

Differentiation is the process in calculus of finding the rate at which a function changes at any given point. It involves applying rules to different types of functions to determine the derivative, which represents the function's instantaneous rate of change.

Derivative of a Logarithmic Function

When differentiating logarithmic functions like the natural logarithm, one applies the rule that the derivative of ln(x) is 1/x for all x greater than zero. This rule is fundamental in dealing with logarithmic expressions in calculus.

Power Rule

The power rule is a basic rule in differentiation that states if a function is in the form x raised to the power of n, its derivative is n times x raised to the power of (n-1). This rule simplifies finding derivatives of polynomial terms.

Constant Rule

The constant rule in differentiation states that the derivative of any constant is zero. Constants do not change with variations in the variable, so they contribute no rate of change in the function.

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