Differentiate the function. v=(√(x)+(1)/(√(x)))^2

Name: Problem 24, Chapter 3: Calculus
Uploaded: 2019-07-01T15:07:39-08:00
Duration: 2 min 22 s
Channel: Clarissa Noh
Description: Differentiate the function. v=(√(x)+(1)/(√(x)))^2

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Key Concepts

Power Rule

The power rule is a fundamental concept in differentiation that simplifies finding the derivative of functions in the form x^n. Both radical expressions in this problem can be rewritten as x raised to a fractional exponent, allowing the power rule to be applied directly in computing their derivatives.

Algebraic Manipulation

Algebraic manipulation is crucial when preparing a function for differentiation. In this case, the function is best handled by rewriting radicals as fractional powers, which not only clarifies the structure of the function but also allows the systematic application of differentiation rules such as the power rule and chain rule.

Chain Rule

The chain rule is used in differentiation when dealing with composite functions, where one function is nested within another. In this particular problem, the function is structured as an outer function (squaring) applied to an inner function (the sum of radical expressions), making the chain rule essential for computing the derivative accurately.

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