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Get Started Now- Lesson: 119:06

In this section, we will learn how to differentiate functions that result from the product of at least two distinct functions using the Product Rule. There are many memory tricks out there that help us remember the Product Rule, the song "hi-de-lo, lo-de-hi", for instance. But since we think they are still a bit too long, we will introduce you a much shorter, cleaner, cooler version – "d.o.o.d" (pronounced as "dude").

1.

Differentiate:

a) $y = {x^5}\sin x$

b) $y = {\left( {6{x^2} + x - 4} \right)^5}\sin 2x$

a) $y = {x^5}\sin x$

b) $y = {\left( {6{x^2} + x - 4} \right)^5}\sin 2x$

24.

Derivatives

24.1

Definition of derivative

24.2

Power rule

24.3

Slope and equation of tangent line

24.4

Chain rule

24.5

Derivative of trigonometric functions

24.6

Derivative of exponential functions

24.7

Product rule

24.8

Quotient rule

24.9

Implicit differentiation

24.10

Derivative of inverse trigonometric functions

24.11

Derivative of logarithmic functions

24.12

Higher order derivatives

24.13

Tangent and concavity of parametric equations

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

Get Started Now24.1

Definition of derivative

24.2

Power rule

24.3

Slope and equation of tangent line

24.4

Chain rule

24.5

Derivative of trigonometric functions

24.6

Derivative of exponential functions

24.7

Product rule

24.8

Quotient rule

24.9

Implicit differentiation

24.10

Derivative of inverse trigonometric functions

24.11

Derivative of logarithmic functions

24.12

Higher order derivatives