IMPLICITE DIFF
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is implicit differentiation?
Back
Implicit differentiation is a technique used to find the derivative of a function that is not explicitly solved for one variable in terms of another.
2.
FLASHCARD QUESTION
Front
How do you find dy/dx using implicit differentiation?
Back
To find dy/dx using implicit differentiation, differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx.
3.
FLASHCARD QUESTION
Front
What does the derivative represent in calculus?
Back
The derivative represents the slope of the tangent line to the curve at a given point.
4.
FLASHCARD QUESTION
Front
What is the formula for the derivative of y with respect to x in the equation 2x^2 - 3y^2 = 4?
Back
The formula is dy/dx = 2x / (3y).
5.
FLASHCARD QUESTION
Front
How do you find dy/dx at a specific point?
Back
To find dy/dx at a specific point, first find the derivative using implicit differentiation, then substitute the coordinates of the point into the derivative.
6.
FLASHCARD QUESTION
Front
What is the derivative of the equation 3x^2 - 5x + 6y^2 - 7y = 24?
Back
The derivative is dy/dx = (-6x + 5) / (12y - 7).
7.
FLASHCARD QUESTION
Front
What is the result of implicit differentiation for the equation x^3 + y^3 = 36?
Back
The result is dy/dx = -x^2 / y^2.
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