Differentiate the function. F(x)=((1)/(2) x)^5

Name: Problem 17, Chapter 3: Calculus
Uploaded: 2020-03-25T23:22:51-08:00
Duration: 48 s
Channel: Amrita Bhasin
Description: Differentiate the function. F(x)=((1)/(2) x)^5

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Key Concepts

Constant Multiple Rule

The constant multiple rule is a differentiation rule that asserts the derivative of a constant times a function is the constant multiplied by the derivative of the function. When a function includes a constant factor, such as in a linear function that is scaled, this rule ensures that the constant is carried through the differentiation process.

Chain Rule

The chain rule is used to differentiate composite functions, where one function is applied inside another. It states that the derivative of the composite function f(g(x)) is f?(g(x)) multiplied by g?(x). In this problem, since the inner function is a linear expression multiplied by a constant, the chain rule is used to multiply the power rule result by the derivative of that inner function.

Power Rule

The power rule is a fundamental principle in differentiation that states if you have a function of the form f(x) = [g(x)]^n, its derivative is n * [g(x)]^(n-1) multiplied by the derivative of g(x). This rule allows you to systematically reduce the exponent while accounting for the function nested inside the power.

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