Find an equation of the tangent line to f(x)=2 lnx^3 |...

Name: Problem 30, Chapter 2: Calculus: Early Transcendental Functions
Uploaded: 2020-06-14T23:35:43-08:00
Duration: 1 min 2 s
Channel: Ernest Castorena
Description: Find an equation of the tangent line to f(x)=2 lnx^3

Key Concepts

Logarithmic Differentiation

Logarithmic differentiation is a technique used to differentiate functions involving logarithms. By applying logarithmic identities, such as converting a logarithm of a power into a product, the differentiation process can be simplified. This is particularly useful when the function includes logarithms of expressions raised to a power.

Point-Slope Form

The point-slope form is a formula used to write the equation of a line when one point on the line and the slope are known. It is expressed as y - y? = m(x - x?), where m is the slope and (x?, y?) is the point on the line. This form is commonly used after finding the derivative to construct the equation of the tangent line.

Derivative

The derivative of a function represents the instantaneous rate of change of the function with respect to its variable. It is fundamental in determining the slope of the tangent line at any given point on the function's graph.

Tangent Line

A tangent line to a curve at a given point is a straight line that just touches the curve at that point, having the same slope as the curve there. It is used as a linear approximation of the function near the point of tangency.

Chain Rule

The chain rule is a method for finding the derivative of composite functions. It states that if a function can be written as f(g(x)), then its derivative is f'(g(x)) multiplied by g'(x). This rule is essential when differentiating functions that involve nested expressions.

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