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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Find first derivative
![Find \(\frac{d}{dx} \left( \sqrt[3]{x \sin(x)} + \sqrt{x + \arctan^2(x^3)} \right)\)
This problem involves finding the derivative of a function that combines cube roots, square roots, and trigonometric as well as inverse trigonometric functions. The expression inside the derivative consists of:
1. A cube root of the product \(x \sin(x)\).
2. A square root of the sum \(x + \arctan^2(x^3)\), where \(\arctan\) is the inverse tangent function.
This example requires using the chain rule, product rule, and the derivatives of trigonometric and inverse trigonometric functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F131cc8df-1e0c-4cc0-a710-15de6c1d2fb3%2F72da53e6-eefd-467a-bd86-0f3f1fbe91ee%2F597lat_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find \(\frac{d}{dx} \left( \sqrt[3]{x \sin(x)} + \sqrt{x + \arctan^2(x^3)} \right)\)
This problem involves finding the derivative of a function that combines cube roots, square roots, and trigonometric as well as inverse trigonometric functions. The expression inside the derivative consists of:
1. A cube root of the product \(x \sin(x)\).
2. A square root of the sum \(x + \arctan^2(x^3)\), where \(\arctan\) is the inverse tangent function.
This example requires using the chain rule, product rule, and the derivatives of trigonometric and inverse trigonometric functions.
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