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: Implicit Differentiation and Slope of a Curve
**Instructions:**
a. Use implicit differentiation to find the derivative \(\frac{dy}{dx}\).
b. Find the slope of the curve at the given point.
**Problem:**
Given the equation:
\[ 3xy + 2x^{3/2}y^{-1/2} = 5, \quad (1, 1) \]
### Tasks:
a. \(\frac{dy}{dx} =\) [ ]
b. The slope of the curve at the point \((1,1)\) is [ ] (Type an integer or a simplified fraction).
**Note:** Enter your answer in each of the answer boxes provided.
For this exercise, you'll be applying the principles of implicit differentiation to solve for the derivative \(\frac{dy}{dx}\), and then calculating the specific slope of the curve at the given point \((1,1)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6636cfe7-e3c3-49e8-b6bc-0fd048d49256%2Fbbd19fbd-c0ed-42e0-a18f-2ab544430a7a%2F0ixbknd.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Exercise: Implicit Differentiation and Slope of a Curve
**Instructions:**
a. Use implicit differentiation to find the derivative \(\frac{dy}{dx}\).
b. Find the slope of the curve at the given point.
**Problem:**
Given the equation:
\[ 3xy + 2x^{3/2}y^{-1/2} = 5, \quad (1, 1) \]
### Tasks:
a. \(\frac{dy}{dx} =\) [ ]
b. The slope of the curve at the point \((1,1)\) is [ ] (Type an integer or a simplified fraction).
**Note:** Enter your answer in each of the answer boxes provided.
For this exercise, you'll be applying the principles of implicit differentiation to solve for the derivative \(\frac{dy}{dx}\), and then calculating the specific slope of the curve at the given point \((1,1)\).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Given function is
Differentiating both sides with respect to x , we get
Step 2
Now, we know that slope of tangent to the curve y=f(x) at the point (a,b) is value of dy/dx at (a,b).
Therefore, slope of tangent to given curve at point (1,1) is
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