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What is implicit differentiation?
Implicit differentiation is a technique for differentiating equations in which the variable to be differentiated is not explicitly defined. It is used to find the derivative of functions that are defined implicitly, such as the functions defined by the equations y2 +x2 =1 and ey +x=y.
Uses of implicit differentiation
Implicit differentiation can be used to solve a variety of problems in calculus, including:
- Finding the slope of the tangent line to a curve at a given point.
- Finding the maximum and minimum values of a function.
- Solving differential equations.
- Modeling real-world phenomena.
Why study implicit differentiation?
Studying implicit differentiation is useful for students looking for a career in mathematics, engineering, physics, economics, and computer science.
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