Find the derivative of each function. y=(3 x+7) ln(2 x-1) |...

Name: Problem 12, Chapter 12: Finite Mathematics and Calculus with Applications
Uploaded: 2020-05-10T19:20:25-08:00
Duration: 3 min 7 s
Channel: Oswaldo Jiménez
Description: Find the derivative of each function. y=(3 x+7) ln(2 x-1)

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Key Concepts

Product Rule

The product rule is essential for differentiating functions that are products of two or more simpler functions. It states that the derivative of a product u(x)v(x) is given by u'(x)v(x) + u(x)v'(x), which allows us to differentiate each component separately and then combine them.

Chain Rule

The chain rule is used to differentiate composite functions, where one function is nested inside another. It states that if a function y = f(g(x)) is composed of an outer function f and an inner function g, then the derivative is f'(g(x)) multiplied by g'(x).

Differentiation of Logarithmic Functions

When differentiating logarithmic functions like ln(u(x)), the derivative is obtained by applying the chain rule, resulting in (1/u(x)) multiplied by u'(x). This concept is crucial when dealing with logarithmic functions that have arguments other than x.

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