ow the steps below for the given function. (Do not use mixed numbers in your answers.) 8x + 5y: we the equation for y. - 8 5x+ 93/5 = 9 erentiate this equation with respect to x. plete the steps below to implicitly take the derivative of the original equation. 8x + 5y = 9 dy dx + dy dx dy dx = 0 || II
ow the steps below for the given function. (Do not use mixed numbers in your answers.) 8x + 5y: we the equation for y. - 8 5x+ 93/5 = 9 erentiate this equation with respect to x. plete the steps below to implicitly take the derivative of the original equation. 8x + 5y = 9 dy dx + dy dx dy dx = 0 || II
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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![### Follow the steps below for the given function. (Do not use mixed numbers in your answers.)
#### Given Equation:
\[ 8x + 5y = 9 \]
#### Solve the equation for \( y \).
\[ y = -\frac{8}{5}x + \frac{9}{5} \]
(corrected)
#### Differentiate this equation with respect to \( x \).
\[ y' = \]
(incorrect, as indicated by a red cross)
#### Complete the steps below to implicitly take the derivative of the original equation.
\[ 8x + 5y = 9 \]
1. \[ \frac{d}{dx}\left(8x\right) + \left(\frac{d}{dx}\left(5y\right)\right)\frac{dy}{dx} = 0 \]
2. Solve for \(\frac{dy}{dx}\):
\[ 8 + 5\frac{dy}{dx} = 0 \]
3. \[ \frac{dy}{dx} = -\frac{8}{5} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ef2aea6-ca63-493c-95d5-a7314878e877%2F460f7589-d28a-4b3e-b0ae-8d04f481ed68%2Ftgrc6tk_processed.png&w=3840&q=75)
Transcribed Image Text:### Follow the steps below for the given function. (Do not use mixed numbers in your answers.)
#### Given Equation:
\[ 8x + 5y = 9 \]
#### Solve the equation for \( y \).
\[ y = -\frac{8}{5}x + \frac{9}{5} \]
(corrected)
#### Differentiate this equation with respect to \( x \).
\[ y' = \]
(incorrect, as indicated by a red cross)
#### Complete the steps below to implicitly take the derivative of the original equation.
\[ 8x + 5y = 9 \]
1. \[ \frac{d}{dx}\left(8x\right) + \left(\frac{d}{dx}\left(5y\right)\right)\frac{dy}{dx} = 0 \]
2. Solve for \(\frac{dy}{dx}\):
\[ 8 + 5\frac{dy}{dx} = 0 \]
3. \[ \frac{dy}{dx} = -\frac{8}{5} \]
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