(To be honest, these aren't so much tricks as they are actual mathematical theorems and rules.)
The first rule should be simple to understand, if you think about it. Take any constant function, f(x) = c. The derivative of this, that is, f'(x), will always be zero.
It's an easy one to remember, and the explanation is easy to visualize as well. If you have a graph of f(x) = c, you basically have a horizontal line that never varies. For every value of x on your curve, f(x) is the same, constant value. So, it has no slope - its slope is zero. Furthermore, if you refer back to my graphical explanation of derivatives in my previous post, you will see that the derivative f'(x) is equal to the slope of f(x). So, if we have a line that has no slope here, we can see how this rule comes together. For fun, you can practice your limit notation and long-hand derivative calculations to prove that this is the case. Refer back again to my last post and use the definition of a derivative. Hint: in your calculation, f(x) = c, and f(x + h) = c.
This is one of the easiest differentiation formulas (if you can call it that) that you are going to encounter, so memorize this one, and get ready for something a little bit more challenging in my next post: the Power Rule.
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