## Friday, February 26, 2016

Here's an example of solving for dy/dx using implicit differentiation

y^2 + 2xy^3 - 3x^2 = 14

2y(dy/dx) + 2x(3y^2)(dy/dx) + 2y^3 - 6x = 0

2y(dy/dx) + 6xy^2(dy/dx) = 6x - 2y^3

dy/dx(2y +6xy^2) = 6x - 2y^3

dy/dx = (6x-2y^3)/(6xy^2 + 2y)

dy/dx = (3x-y^3)/(3xy^2 + y)
The text passage provides a step-by-step solution to a calculus problem involving implicit differentiation. It shows the process of finding the derivative \( \frac{dy}{dx} \) for a given equation.
no_question
- the passage does not contain a question but rather a worked example of a mathematical problem.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Friday, February 26, 2016

Here's an example of solving for dy/dx using implicit differentiation

y^2 + 2xy^3 - 3x^2 = 14

2y(dy/dx) + 2x(3y^2)(dy/dx) + 2y^3 - 6x = 0

2y(dy/dx) + 6xy^2(dy/dx) = 6x - 2y^3

dy/dx(2y +6xy^2) = 6x - 2y^3

dy/dx = (6x-2y^3)/(6xy^2 + 2y)

dy/dx = (3x-y^3)/(3xy^2 + y)
user
The text passage provides a step-by-step solution to a calculus problem involving implicit differentiation. It shows the process of finding the derivative \( \frac{dy}{dx} \) for a given equation.

TYPE: NO_QUESTION
- The passage does not contain a question but rather a worked example of a mathematical problem.