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Implicit differentiation
- Intro Lesson9:12
- Lesson: 131:30
- Lesson: 226:14
Implicit differentiation
So far, we have always tried to configure a relation to an explicit function in the form of y = f(x) before finding the derivative of the relation, but what if this is impossible to do so? In this section, we will first learn to identify the difference between explicit functions and implicit functions. Then we will learn how to differentiate a relation with a mix of variables x and y using the method called Implicit Differentiation.
Lessons
- IntroductionExplicit Functions VS. Implicit Functions
- 1.The graph shows a circle centred at the origin with a radius of 5.
a) Define the circle implicitly by a relation between x and y .
b) Define the circle by expressing y explicitly in terms of x .
c) Use the method of "explicit differentiation" to find the slope of the tangent line to the circle at the point (4, -3).
d) Use the method of "implicit differentiation" to find the slope of the tangent line to the circle at the point (4, -3). - 2.3y4+5x2y3−x6=2x−9y+1
Use implicit differentiation to find: dxdy
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26.
Limits and Derivatives
26.1
Finding limits from graphs
26.2
Definition of derivative
26.3
Power rule
26.4
Slope and equation of tangent line
26.5
Chain rule
26.6
Derivative of trigonometric functions
26.7
Derivative of exponential functions
26.8
Product rule
26.9
Quotient rule
26.10
Implicit differentiation
26.11
Derivative of inverse trigonometric functions
26.12
Derivative of logarithmic functions
26.13
Higher order derivatives
Don't just watch, practice makes perfect
Practice topics for Limits and Derivatives
26.1
Finding limits from graphs
26.2
Definition of derivative
26.3
Power rule
26.4
Slope and equation of tangent line
26.5
Chain rule
26.6
Derivative of trigonometric functions
26.7
Derivative of exponential functions
26.8
Product rule
26.9
Quotient rule
26.10
Implicit differentiation
26.11
Derivative of inverse trigonometric functions
26.12
Derivative of logarithmic functions
26.13
Higher order derivatives