Implicit Differentiation

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•
Mathematics
•
11th Grade
•
Hard
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15 questions
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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 defined implicitly by an equation involving both x and y, rather than explicitly solving for y.
2.
FLASHCARD QUESTION
Front
How do you apply implicit differentiation to an equation?
Back
To apply implicit differentiation, differentiate both sides of the equation with respect to x, treating y as a function of x. Use the chain rule for terms involving y.
3.
FLASHCARD QUESTION
Front
What is the derivative of y with respect to x denoted as?
Back
The derivative of y with respect to x is denoted as dy/dx.
4.
FLASHCARD QUESTION
Front
What is the chain rule in the context of implicit differentiation?
Back
The chain rule states that if y is a function of x, then the derivative of y with respect to x is the derivative of y with respect to y times the derivative of y with respect to x.
5.
FLASHCARD QUESTION
Front
Given the equation xy + y^2 = 2, how do you find dy/dx?
Back
Differentiate both sides with respect to x: d(xy)/dx + d(y^2)/dx = d(2)/dx. Apply the product rule for xy and the chain rule for y^2.
6.
FLASHCARD QUESTION
Front
What is the product rule?
Back
The product rule states that if u and v are functions of x, then d(uv)/dx = u(dv/dx) + v(du/dx).
7.
FLASHCARD QUESTION
Front
How do you differentiate y^2 with respect to x?
Back
Using the chain rule, d(y^2)/dx = 2y(dy/dx).
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