Friday, May 17, 2013

Differentiation Rules - Finding the Derivative of a Difference of Functions

This post continues along in my series on calculus differentiation rules, this time talking about how to find the derivative of a difference of functions. I hope you read my last post, which applied to sums of functions, because it is nearly the same situation when you are subtracting. I'm not going to go into the same level as detail as I did there, so I highly recommend you go back and give that a read, and then come back here to see how the same kind of thing applies.

Recall the setup for these rules. Let f(x) and g(x) be two separate functions (anything you want), and let's also say that the sum of these functions, that is, f(x) + g(x), is equal to F(x). Similarly, let's say that the difference of these functions, that is, f(x) - g(x), is represented by G(x).

To find the derivative of a difference of functions, you simply determine the derivatives of the component functions and subtract them accordingly to get G'(x).

Therefore: the derivative of a difference of functions is equal to the difference of those functions' derivatives.

Compare this to the differentiation rule for adding that I covered last time. You can see how it's the same kind of thing, with no extra manipulations or reorganizations or tricks. If you can add, then you can subtract.

I'm not going to provide any examples for this rule, unless anyone leaves me a comment below to specifically request some. I think that if you can work through the example for adding, you will have a good grasp of how to perform both the addition and subtraction differentiation rules.

Thanks for checking out my latest post, even though this is one of my shorter ones. I always love getting feedback, and Facebook Likes and +1's are very much appreciated!

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