Compute the derivative. f(θ)=θtanθsecθ

Name: Problem 20, Chapter 3: Calculus: Early Transcendentals
Uploaded: 2021-07-13T00:12:58-08:00
Duration: 1 min 48 s
Channel: Kian Manafi
Description: Compute the derivative. f(θ)=θtanθsecθ

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Key Concepts

Trigonometric Derivative Formulas

This key concept involves knowing the standard derivatives of trigonometric functions, which is critical when differentiating functions involving trigonometric expressions. For instance, the derivative of tan(?) is sec²(?), and the derivative of sec(?) is sec(?)tan(?). These formulas allow for the systematic differentiation of trigonometric functions.

Simplification Using Trigonometric Identities

After differentiating an expression, one often needs to simplify the result to a more manageable or insightful form. In the context of trigonometric functions, this involves using identities such as sec²(?) - tan²(?) = 1. Recognizing and applying these identities can significantly simplify the final derivative expression and reveal deeper relationships among the trigonometric components.

Product Rule

The product rule is a fundamental concept in differential calculus used to find the derivative of the product of two functions. It states that if you have two functions, u(?) and v(?), then the derivative of their product is given by u'(?)v(?) + u(?)v'(?). This rule is essential when differentiating complex expressions where two or more functions are multiplied together.

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