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

2.

Differentiation

2.1

Definition of derivative

2.2

Estimating derivatives from a table

2.3

Power rule

2.4

Slope and equation of tangent line

2.5

Chain rule

2.6

Derivative of trigonometric functions

2.7

Derivative of exponential functions

2.8

Product rule

2.9

Quotient rule

2.10

Implicit differentiation

2.11

Derivative of inverse trigonometric functions

2.12

Derivative of logarithmic functions

2.13

Higher order derivatives

We have over 170 practice questions in Calculus 1 for you to master.

Get Started Now2.1

Definition of derivative

2.3

Power rule

2.4

Slope and equation of tangent line

2.5

Chain rule

2.6

Derivative of trigonometric functions

2.7

Derivative of exponential functions

2.8

Product rule

2.9

Quotient rule

2.10

Implicit differentiation

2.11

Derivative of inverse trigonometric functions

2.12

Derivative of logarithmic functions

2.13

Higher order derivatives