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dy Find for the function y = 11*.

dy Find for the function y = 11*.

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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Question
**Problem Statement:** Find \(\frac{dy}{dx}\) for the function \(y = 11^x\). --- **Solution:** The problem requires finding the derivative of the exponential function \(y = 11^x\) with respect to \(x\). **Step-by-Step Explanation:** 1. **Identify the Function:** - The function given is \(y = 11^x\). 2. **Apply the Derivative Rules for Exponential Functions:** - The derivative of \(a^x\) with respect to \(x\) is given by \(\frac{d}{dx}(a^x) = a^x \ln(a)\). - In this case, \(a = 11\). 3. **Calculate the Derivative:** - \(\frac{dy}{dx} = 11^x \ln(11)\). The derivative of the function \(y = 11^x\) is \(\frac{dy}{dx} = 11^x \ln(11)\). **Conclusion:** The derivative \(\frac{dy}{dx}\) for the function \(y = 11^x\) is \(11^x \ln(11)\).
Transcribed Image Text:**Problem Statement:** Find \(\frac{dy}{dx}\) for the function \(y = 11^x\). --- **Solution:** The problem requires finding the derivative of the exponential function \(y = 11^x\) with respect to \(x\). **Step-by-Step Explanation:** 1. **Identify the Function:** - The function given is \(y = 11^x\). 2. **Apply the Derivative Rules for Exponential Functions:** - The derivative of \(a^x\) with respect to \(x\) is given by \(\frac{d}{dx}(a^x) = a^x \ln(a)\). - In this case, \(a = 11\). 3. **Calculate the Derivative:** - \(\frac{dy}{dx} = 11^x \ln(11)\). The derivative of the function \(y = 11^x\) is \(\frac{dy}{dx} = 11^x \ln(11)\). **Conclusion:** The derivative \(\frac{dy}{dx}\) for the function \(y = 11^x\) is \(11^x \ln(11)\).
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y=11^x

take derivative

\frac{dy}{dx}=\frac{d}{dx}\left(11^x\right)

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