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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: $\frac{{{d}y}}{{{d}x}}$

25.

Derivatives

25.1

Definition of derivative

25.2

Power rule

25.3

Gradient and equation of tangent line

25.4

Chain rule

25.5

Derivative of trigonometric functions

25.6

Derivative of exponential functions

25.7

Product rule

25.8

Quotient rule

25.9

Implicit differentiation

25.10

Derivative of inverse trigonometric functions

25.11

Derivative of logarithmic functions

25.12

Higher order derivatives

We have over 860 practice questions in Sixth Year Maths for you to master.

Get Started Now25.1

Definition of derivative

25.2

Power rule

25.3

Gradient and equation of tangent line

25.4

Chain rule

25.5

Derivative of trigonometric functions

25.6

Derivative of exponential functions

25.7

Product rule

25.8

Quotient rule

25.9

Implicit differentiation

25.10

Derivative of inverse trigonometric functions

25.11

Derivative of logarithmic functions

25.12

Higher order derivatives