Product rule

Product rule

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").

Lessons


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  • 1.
    Differentiate:
    a) y=x5sin⁡xy = {x^5}\sin x
    b) y=(6x2+x−4)5sin⁡2xy = {\left( {6{x^2} + x - 4} \right)^5}\sin 2x
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    24.
    Derivatives
    24.1
    Definition of derivative
    24.2
    Power rule
    24.3
    Gradient 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
    Sixth Year Maths
    Don't just watch, practice makes perfect.