Implicit Differentiation
Definition
Implicit differentiation is a technique used to differentiate an equation implicitly without explicitly solving for one variable in terms of another.
Analogy
Imagine trying to differentiate a cake recipe where some ingredients are mixed together but not explicitly stated. Implicit differentiation helps us find how changing one ingredient affects another without separating them completely.
Related terms
Chain Rule: The chain rule is used in calculus to find derivatives when functions are composed or nested within each other.
Related Rates: Related rates involve finding how two quantities change with respect to time when they are related by an equation.
Tangent Line: A tangent line is a line that touches a curve at only one point and has the same slope as the curve at that point.
"Implicit Differentiation" appears in:
Study guides (3)
Additional resources (4)
Practice Questions (14)
What notation is commonly used for derivatives in implicit differentiation?
What are the three main steps of implicit differentiation?
Which step of implicit differentiation involves factoring out y'?
What should be isolated in the final step of implicit differentiation?
What is the derivative of the equation y = x^3 + 2x, obtained through implicit differentiation?
Which of the following equations represents implicit differentiation?
What is the derivative of the equation x^2 + y^2 = 9, obtained through implicit differentiation?
Which of the following equations requires implicit differentiation to find the derivative?
Find the derivative of y with respect to x for the equation x^2 + 2xy + y^2 = 25 using implicit differentiation:
What is implicit differentiation used for?
What is the first step in implicit differentiation?
Which of the following is an advantage of implicit differentiation?
Which of the following is an application of implicit differentiation?
What is the main advantage of using implicit differentiation?
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