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

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