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Find the derivative dy dx of the function y = sec +√4+ sin (4+x²) + x²)).

Find the derivative dy dx of the function y = sec +√4+ sin (4+x²) + x²)).

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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**Calculus Exercise: Finding the Derivative** **Problem Statement:** Find the derivative \(\frac{dy}{dx}\) of the function \( y = \sec \left( 1 + \sqrt[3]{4} + \sin^{-1} (4 + \pi^2) \right) \). **Solution:** \(\frac{dy}{dx} = \) [Please input your derivative solution in the provided box.] --- **Explanation:** This exercise involves finding the derivative of a composite trigonometric function. The function \( y \) is given as the secant of a combination of constants and a trigonometric inverse function. 1. **Identify the components:** - The inner function consists of constant values and expressions, including a cube root and an inverse sine function. - The outer function is the secant function, \( \sec(u) \). 2. **Apply the chain rule:** - You will need to differentiate the outer function (\( \sec(u) \)) with respect to the inner function (\( u \)). - Then, differentiate the inner function with respect to \( x \). This problem is designed to test your understanding of derivatives, particularly using the chain rule with trigonometric and inverse trigonometric functions.
Transcribed Image Text:**Calculus Exercise: Finding the Derivative** **Problem Statement:** Find the derivative \(\frac{dy}{dx}\) of the function \( y = \sec \left( 1 + \sqrt[3]{4} + \sin^{-1} (4 + \pi^2) \right) \). **Solution:** \(\frac{dy}{dx} = \) [Please input your derivative solution in the provided box.] --- **Explanation:** This exercise involves finding the derivative of a composite trigonometric function. The function \( y \) is given as the secant of a combination of constants and a trigonometric inverse function. 1. **Identify the components:** - The inner function consists of constant values and expressions, including a cube root and an inverse sine function. - The outer function is the secant function, \( \sec(u) \). 2. **Apply the chain rule:** - You will need to differentiate the outer function (\( \sec(u) \)) with respect to the inner function (\( u \)). - Then, differentiate the inner function with respect to \( x \). This problem is designed to test your understanding of derivatives, particularly using the chain rule with trigonometric and inverse trigonometric functions.
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