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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how do i solve this chain rule question?
![**Calculate the derivative using implicit differentiation:**
Given the equation:
\[ x^3 w + w^8 + w^2 + 7yz = 0 \]
We are asked to find the partial derivative of \( w \) with respect to \( z \), denoted as \( \frac{\partial w}{\partial z} \).
The solution for the derivative is:
\[
\frac{\partial w}{\partial z} = \frac{-2w - 7y}{\left(x^3 + 8w + 2z\right)}
\]
The derivation involves using implicit differentiation to solve for \( \frac{\partial w}{\partial z} \) in terms of the given variables and expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3cfeff4-8ba6-46a8-98d4-804b4f4f620a%2F432c5966-2c50-4beb-aaf6-3045f32f6a32%2Fvood96l_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculate the derivative using implicit differentiation:**
Given the equation:
\[ x^3 w + w^8 + w^2 + 7yz = 0 \]
We are asked to find the partial derivative of \( w \) with respect to \( z \), denoted as \( \frac{\partial w}{\partial z} \).
The solution for the derivative is:
\[
\frac{\partial w}{\partial z} = \frac{-2w - 7y}{\left(x^3 + 8w + 2z\right)}
\]
The derivation involves using implicit differentiation to solve for \( \frac{\partial w}{\partial z} \) in terms of the given variables and expressions.
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