3-2 Implicit Differentiation

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•
Mathematics
•
11th - 12th Grade
•
Hard
Standards-aligned
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1.
FLASHCARD QUESTION
Front
What is implicit differentiation?
Back
Implicit differentiation is a technique used to differentiate equations that define y implicitly in terms of x, rather than explicitly as y = f(x).
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 is the derivative of y^2 with respect to x?
Back
The derivative of y^2 with respect to x is 2y(dy/dx) due to the chain rule.
4.
FLASHCARD QUESTION
Front
What is the chain rule in differentiation?
Back
The chain rule states that if a function y is composed of another function u, then the derivative of y with respect to x is dy/dx = dy/du * du/dx.
5.
FLASHCARD QUESTION
Front
How do you differentiate the equation xy + y^2 = 2?
Back
Differentiate both sides: d/dx(xy) + d/dx(y^2) = d/dx(2). This gives y + x(dy/dx) + 2y(dy/dx) = 0.
6.
FLASHCARD QUESTION
Front
What is the result of differentiating x^3 + y^3 = 36?
Back
Differentiating gives 3x^2 + 3y^2(dy/dx) = 0, which can be rearranged to find dy/dx.
7.
FLASHCARD QUESTION
Front
What does dy/dx represent in a function?
Back
dy/dx represents the rate of change of y with respect to x, or the slope of the tangent line to the curve at a given point.
Tags
CCSS.HSF.LE.B.5
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