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

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