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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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17.
Derivatives
17.1
Definition of derivative
17.2
Power rule
17.3
Gradient and equation of tangent line
17.4
Chain rule
17.5
Derivative of trigonometric functions
17.6
Derivative of exponential functions
17.7
Product rule
17.8
Quotient rule
17.9
Implicit differentiation
17.10
Derivative of inverse trigonometric functions
17.11
Derivative of logarithmic functions
17.12
Higher order derivatives
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Practice topics for Derivatives
17.1
Definition of derivative
17.2
Power rule
17.3
Gradient and equation of tangent line
17.4
Chain rule
17.5
Derivative of trigonometric functions
17.6
Derivative of exponential functions
17.7
Product rule
17.8
Quotient rule
17.9
Implicit differentiation
17.10
Derivative of inverse trigonometric functions
17.11
Derivative of logarithmic functions
17.12
Higher order derivatives