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Related Rates
Types of related rates, implicit differentiation
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Exercises
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Types of related rates, implicit differentiation
Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)
No exercises available for this concept.
Given three variables x, y, and z,
Hence, given dzdx, we can find an expression for dzdy by calculating dxdy.
Implicit differentiation is when we differentiate both sides of an equation. It is helpful when we have an equation that cannot be simplified to y=f(x).
Since dtdy=dxdy⋅dtdx, you may be asked to use implicit differentiation to find dxdy, then with a given dtdx and point, you can find dtdy.
Given the time rate of change of radius, length, height, or width of a three dimensional object, you may find the time rate of change of volume by taking the derivative of the volume equation.
Let L be the distance from the origin of a point with coordinates (x,y). Then, given dtdx and dtdy, we can find dtdL at a given point (x,y).
Using a given rate of change dtdx and trigonometry, we can calculate dxdθ, which can be used to find dtdθ.