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10. f(x) = tan² (4x³ - 1)

10. f(x) = tan² (4x³ - 1)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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10.) find derivative
10. \( f(x) = \tan^2(4x^3 - 1) \) This function represents the square of the tangent of the expression \(4x^3 - 1\). The tangent function, denoted as \(\tan\), is a trigonometric function that relates the angles of a right triangle to the ratio of the length of the opposite side to the adjacent side. In this case, the tangent function is squared, which means after computing \(\tan(4x^3 - 1)\), you multiply the result by itself to get \(\tan^2(4x^3 - 1)\).
Transcribed Image Text:10. \( f(x) = \tan^2(4x^3 - 1) \) This function represents the square of the tangent of the expression \(4x^3 - 1\). The tangent function, denoted as \(\tan\), is a trigonometric function that relates the angles of a right triangle to the ratio of the length of the opposite side to the adjacent side. In this case, the tangent function is squared, which means after computing \(\tan(4x^3 - 1)\), you multiply the result by itself to get \(\tan^2(4x^3 - 1)\).
Expert Solution
Step 1

Given f(x)=tan^2(4x^3-1)

We will find the derivation of f(x) as shown below 

 

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