Use logarithmic differentiation to find the derivative of the function. y=((2 x^2-1)^5)/(√(x+1))

Name: Problem 45, Chapter 5: Applied Calculus for the Managerial, Life, and Social Sciences
Uploaded: 2021-05-11T08:27:07-08:00
Duration: 4 min 47 s
Channel: Priyanka Sadarangani
Description: Use logarithmic differentiation to find the derivative of the function. y=((2 x^2-1)^5)/(√(x+1))

step 1 Okay, and this question of function is given, that is y equals to 2x square minus 1 raised to th

Use logarithmic differentiation to find the derivative of...

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Key Concepts

Chain Rule

The chain rule is a fundamental tool for differentiating composite functions. When applying logarithmic differentiation, many of the functions involved are composed of inner and outer functions, so the chain rule is used to correctly differentiate these compositions.

Implicit Differentiation

Implicit differentiation is used when differentiating equations where the dependent variable is not isolated. In logarithmic differentiation, after taking the natural logarithm of both sides, one differentiates both sides with respect to the independent variable, applying implicit differentiation as necessary.

Properties of Logarithms

The properties of logarithms, such as the product rule, quotient rule, and power rule, are essential when applying logarithmic differentiation. They allow for the decomposition of complex expressions into simpler parts, thereby simplifying the differentiation process.

Logarithmic Differentiation

Logarithmic differentiation is a method used to differentiate functions by taking the natural logarithm of both sides of an equation. This transforms products, quotients, and powers into sums, differences, and multiples, making it easier to differentiate complex expressions.

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