Find d y / d x. y=√(tan5 x)

Name: Problem 24, Chapter 4: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2021-08-28T07:41:12-08:00
Duration: 1 min 5 s
Channel: Adrian Co
Description: Find d y / d x. y=√(tan5 x)

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Key Concepts

Chain Rule

The chain rule is a fundamental differentiation technique used when dealing with composite functions. It states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function. This is essential when differentiating functions where one function is nested inside another.

Derivative of a Square Root Function

The derivative of a square root function, such as y = ?u, can be found using the power rule by rewriting the square root as u^(1/2). Its derivative becomes (1/(2?u)) multiplied by the derivative of u. This rule is crucial when the function inside the square root is itself a function of x.

Trigonometric Function Differentiation

Differentiating trigonometric functions like tan(x) involves applying specific rules where, for example, the derivative of tan(u) is sec^2(u) multiplied by the derivative of u. This is important when the argument of the tangent function is a linear function or another composite function, and it ties in with the chain rule for handling such compositions.

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