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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    26.
    Limits and Derivatives
    26.1
    Finding limits from graphs
    26.2
    Definition of derivative
    26.3
    Power rule
    26.4
    Slope and equation of tangent line
    26.5
    Chain rule
    26.6
    Derivative of trigonometric functions
    26.7
    Derivative of exponential functions
    26.8
    Product rule
    26.9
    Quotient rule
    26.10
    Implicit differentiation
    26.11
    Derivative of inverse trigonometric functions
    26.12
    Derivative of logarithmic functions
    26.13
    Higher order derivatives
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