2. D8: I can compute derivatives using multiple rules in combination. D9: I can compute derivatives of implicitly defined functions. (a) You are a tutor in the calculus center and three students come to you with questions about d cos(xy). How would you help these students find and learn from their mistakes? (You may wish to reference the rubrics above to help identify mistakes.) dx Hugh Manatee's answer: d cos(xy) = sin(y + x) dx (b) Emboldened by your thoughtful assistance, Hugh, Dee and Bob give their final answers to the problem below. Decide which answer, if any, is correct and briefly explain why. dy Find given that cos(xy) = sin(ln(y)) with y > 0. dx i. Hugh: sin(xy) (y + x- dy dx ii. Bob: iii. Dee: Dee Rivative's answer: dx cos(xy) = sin(xy) (y + x) dx dy dx sin (cy)y x-cos(ln(y)) 1 dy y dx cos(ln(y)); sin(xy)y - sin(xy)x - cos (ln(y)) Bob the Iguana's answer: cos(xy) = sin(xy) (1) d dx dx
2. D8: I can compute derivatives using multiple rules in combination. D9: I can compute derivatives of implicitly defined functions. (a) You are a tutor in the calculus center and three students come to you with questions about d cos(xy). How would you help these students find and learn from their mistakes? (You may wish to reference the rubrics above to help identify mistakes.) dx Hugh Manatee's answer: d cos(xy) = sin(y + x) dx (b) Emboldened by your thoughtful assistance, Hugh, Dee and Bob give their final answers to the problem below. Decide which answer, if any, is correct and briefly explain why. dy Find given that cos(xy) = sin(ln(y)) with y > 0. dx i. Hugh: sin(xy) (y + x- dy dx ii. Bob: iii. Dee: Dee Rivative's answer: dx cos(xy) = sin(xy) (y + x) dx dy dx sin (cy)y x-cos(ln(y)) 1 dy y dx cos(ln(y)); sin(xy)y - sin(xy)x - cos (ln(y)) Bob the Iguana's answer: cos(xy) = sin(xy) (1) d dx dx
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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![**Problem 2: Calculus Differentiation Questions**
**D8:** I can compute derivatives using multiple rules in combination.
**D9:** I can compute derivatives of implicitly defined functions.
**(a)** You are a tutor in the calculus center, and three students come to you with questions about \(\frac{d}{dx} \cos(xy)\). How would you help these students find and learn from their mistakes? (You may wish to reference the rubrics above to help identify mistakes.)
- **Hugh Manatee’s answer:**
\[
\frac{d}{dx} \cos(xy) = -\sin(y + x)
\]
- **Dee Rivative’s answer:**
\[
\frac{d}{dx} \cos(xy) = -\sin(xy)(y + x)
\]
- **Bob the Iguana’s answer:**
\[
\frac{d}{dx} \cos(xy) = -\sin(xy)\left(\frac{1}{y} \frac{d}{dx}\right)
\]
---
**(b)** Emboldened by your thoughtful assistance, Hugh, Dee, and Bob give their final answers to the problem below. Decide which answer, if any, is correct and briefly explain why.
Find \(\frac{dy}{dx}\) given that \(\cos(xy) = \sin(\ln(y))\) with \(y > 0\).
i. **Hugh:**
\[
-\sin(xy) \left( y + x \frac{dy}{dx} \right) = \cos(\ln(y)) \frac{1}{y} \frac{dy}{dx}
\]
ii. **Bob:**
\[
\frac{dy}{dx} = \frac{\sin(xy)y}{x - \cos(\ln(y)) \frac{1}{y}}
\]
iii. **Dee:**
\[
\frac{dy}{dx} = \frac{\sin(xy)y}{-\sin(xy)x - \cos(\ln(y)) \frac{1}{y}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1b1d143-3544-4565-ae01-c2b2100e15ce%2F96fafecb-763d-4b39-9c60-3357b19e13fb%2F3r86hyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2: Calculus Differentiation Questions**
**D8:** I can compute derivatives using multiple rules in combination.
**D9:** I can compute derivatives of implicitly defined functions.
**(a)** You are a tutor in the calculus center, and three students come to you with questions about \(\frac{d}{dx} \cos(xy)\). How would you help these students find and learn from their mistakes? (You may wish to reference the rubrics above to help identify mistakes.)
- **Hugh Manatee’s answer:**
\[
\frac{d}{dx} \cos(xy) = -\sin(y + x)
\]
- **Dee Rivative’s answer:**
\[
\frac{d}{dx} \cos(xy) = -\sin(xy)(y + x)
\]
- **Bob the Iguana’s answer:**
\[
\frac{d}{dx} \cos(xy) = -\sin(xy)\left(\frac{1}{y} \frac{d}{dx}\right)
\]
---
**(b)** Emboldened by your thoughtful assistance, Hugh, Dee, and Bob give their final answers to the problem below. Decide which answer, if any, is correct and briefly explain why.
Find \(\frac{dy}{dx}\) given that \(\cos(xy) = \sin(\ln(y))\) with \(y > 0\).
i. **Hugh:**
\[
-\sin(xy) \left( y + x \frac{dy}{dx} \right) = \cos(\ln(y)) \frac{1}{y} \frac{dy}{dx}
\]
ii. **Bob:**
\[
\frac{dy}{dx} = \frac{\sin(xy)y}{x - \cos(\ln(y)) \frac{1}{y}}
\]
iii. **Dee:**
\[
\frac{dy}{dx} = \frac{\sin(xy)y}{-\sin(xy)x - \cos(\ln(y)) \frac{1}{y}}
\]
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