Implicit differentiation
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Flip to reveal answersIn implicit differentiation, what happens when you differentiate a y-term w.r.t. x?
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All 8 Flashcards — Implicit differentiation
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Question
In implicit differentiation, what happens when you differentiate a y-term w.r.t. x?
Answer
It picks up a factor of dy/dx (the chain rule), because y is treated as a function of x.
Question
d/dx(y²) = ?
Answer
2y·dy/dx.
Question
How do you differentiate a term like xy w.r.t. x?
Answer
Product rule: y + x·dy/dx.
Question
After differentiating implicitly, how do you isolate dy/dx?
Answer
Collect all dy/dx terms on one side, factor out dy/dx, then divide.
Question
dy/dx for x² + y² = 25?
Answer
2x + 2y·dy/dx = 0 ⇒ dy/dx = −x/y.
Question
How do you find a gradient at a specific point on an implicit curve?
Answer
Substitute the point's x and y values into the expression for dy/dx.
Question
When is the tangent to an implicit curve horizontal? Vertical?
Answer
Horizontal when the numerator of dy/dx is 0; vertical when the denominator is 0 (gradient undefined).
Question
Equation of a tangent once you have m at (x₁, y₁)?
Answer
y − y₁ = m(x − x₁).
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Full study notes for Implicit differentiation
Topic 5.14 hub
Implicit & related rates (HL only)
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