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Get Started Now- Intro Lesson9:12
- Lesson: 131:30
- Lesson: 226:14

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.

- 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.$3{y^4} + 5{x^2}{y^3} - {x^6} = 2x - 9y + 1$

Use implicit differentiation to find: $\frac{{{d}y}}{{{d}x}}$

29.

Derivatives

29.1

Definition of derivative

29.2

Power rule

29.3

Gradient and equation of tangent line

29.4

Chain rule

29.5

Derivative of trigonometric functions

29.6

Derivative of exponential functions

29.7

Product rule

29.8

Quotient rule

29.9

Implicit differentiation

29.10

Derivative of inverse trigonometric functions

29.11

Derivative of logarithmic functions

29.12

Higher order derivatives

We have over 1040 practice questions in AU Year 12 Maths for you to master.

Get Started Now29.1

Definition of derivative

29.2

Power rule

29.3

Gradient and equation of tangent line

29.4

Chain rule

29.5

Derivative of trigonometric functions

29.6

Derivative of exponential functions

29.7

Product rule

29.8

Quotient rule

29.9

Implicit differentiation

29.10

Derivative of inverse trigonometric functions

29.11

Derivative of logarithmic functions

29.12

Higher order derivatives