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Implicit differentiation allows us to find slopes of tangents to curves that are clearly not functions (they fail the vertical line test). We are using the idea that portions of y y are functions that satisfy the given equation, but that y y is not actually a function of x . x .
16 Νοε 2022 · Here is a set of practice problems to accompany the Implicit Differentiation section of the Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University.
29 Δεκ 2020 · Implicit differentiation is a technique based on the Chain Rule that is used to find a derivative when the relationship between the variables is given implicitly rather than explicitly (solved for one variable in terms of the other).
How to do Implicit Differentiation. Differentiate with respect to x. Collect all the dy dx on one side. Solve for dy dx. Example: x 2 + y 2 = r 2. Differentiate with respect to x: d dx (x 2) + d dx (y 2) = d dx (r 2) Let's solve each term: Use the Power Rule: d dx (x2) = 2x. Use the Chain Rule (explained below): d dx (y2) = 2y dy dx.
To find the implicit derivative, take the derivative of both sides of the equation with respect to the independent variable then solve for the derivative of the dependent variable with respect to the independent variable.
Understanding implicit differentiation through examples and graphs and over 10 interactive practice problems explained step by step .
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