Say you have a function like this one:

_{}

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The product rule simply states that if the function can be split up into a sub-function multiplied by another sub-function, then:

_{}

Here u and v are the sub-functions, and _{} and _{} are their
derivatives with respect to x.

Remember:

_{}

Here’s an example of using the product rule:

Find the derivative of |

Solution |

Let
u = 3x Let
v = 2x Then: So: This you can then expand out and simplify to give: |

Be careful when you write ‘u’ and ‘v’ – it is easy to mix them up! You could use the letters ‘a’ and ‘b’ just as easily, ‘u’ and ‘v’ are used here because many textbooks use them.