Given the equation below, find || dy dx Now, find the equation of the tangent line to the curve at (1, 1). Write your answer in mx + b format y = Question Help: Video dy dx Submit Question 30 15x¹ + 9x³0y+y6 = 25
Given the equation below, find || dy dx Now, find the equation of the tangent line to the curve at (1, 1). Write your answer in mx + b format y = Question Help: Video dy dx Submit Question 30 15x¹ + 9x³0y+y6 = 25
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 Statement:**
Given the equation below, find \(\frac{dy}{dx}\).
\[ 15x^4 + 9x^{30}y + y^6 = 25 \]
\[ \frac{dy}{dx} = \]
Now, find the equation of the tangent line to the curve at (1, 1). Write your answer in \(mx + b\) format.
\[ y = \]
**Instructions:**
1. Differentiate the given equation implicitly to solve for \(\frac{dy}{dx}\).
2. Use the derivative to find the slope of the tangent line at the given point (1, 1).
3. Construct the equation of the tangent line using the point-slope form and convert it to \(y = mx + b\) form.
**Resources:**
- **Question Help:** [Video]
- **Action:** Submit your answer via the “Submit Question” button.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b01f764-cc95-4783-8fec-cdda5efc483b%2Ff8d90211-0be3-4e4c-aa4a-bafa766d284d%2F9z15aa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given the equation below, find \(\frac{dy}{dx}\).
\[ 15x^4 + 9x^{30}y + y^6 = 25 \]
\[ \frac{dy}{dx} = \]
Now, find the equation of the tangent line to the curve at (1, 1). Write your answer in \(mx + b\) format.
\[ y = \]
**Instructions:**
1. Differentiate the given equation implicitly to solve for \(\frac{dy}{dx}\).
2. Use the derivative to find the slope of the tangent line at the given point (1, 1).
3. Construct the equation of the tangent line using the point-slope form and convert it to \(y = mx + b\) form.
**Resources:**
- **Question Help:** [Video]
- **Action:** Submit your answer via the “Submit Question” button.
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