Still Confused?

Try reviewing these fundamentals first.

- Home
- UK Year 13 Maths
- Derivatives

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

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

23.

Derivatives

23.1

Definition of derivative

23.2

Power rule

23.3

Slope and equation of tangent line

23.4

Chain rule

23.5

Derivative of trigonometric functions

23.6

Derivative of exponential functions

23.7

Product rule

23.8

Quotient rule

23.9

Implicit differentiation

23.10

Derivative of inverse trigonometric functions

23.11

Derivative of logarithmic functions

23.12

Higher order derivatives

23.13

Tangent and concavity of parametric equations

We have over 760 practice questions in UK Year 13 Maths for you to master.

Get Started Now23.1

Definition of derivative

23.2

Power rule

23.3

Slope and equation of tangent line

23.4

Chain rule

23.5

Derivative of trigonometric functions

23.6

Derivative of exponential functions

23.7

Product rule

23.8

Quotient rule

23.9

Implicit differentiation

23.10

Derivative of inverse trigonometric functions

23.11

Derivative of logarithmic functions

23.12

Higher order derivatives