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The symbols I will use in this installment are the following:

[math]f(x), g(x), h(x) are functions of x.
[math]k is a constant.

Now we have already seen the Sum Rule for differentiation. But let's go over it again:



Which means that if we have to differentiate a function made of the addition of two functions, then its derivative will be made of the addition of the derivatives of the two functions. And this works for more than two functions.

Next one for today is the Constant Multiple rule:



Let's do an example of this. Let's just say we have the following function to differentiate:



We have: [math]k=4, f(x)=x^2+2x. Then its derivative will be:



Last for today will be how to differentiate two functions that are multiplied with each other, or the Product Rule of Differentiation. The product rule is:



The derivative of two functions that are being multiplied with each other, is equal to the derivative of the first function multiplied by the second function, plus the first function multiplied with the derivative of the second function. An example will help you understand this more clearly, and don't forget to ask any pertinent questions in the discussion thread.

Our example is the following:



Here we have: [math]k=5, f(x)=x^7 and\space g(x)=\sin {5x}. Following the rules of differentiation then:




Tomorrow I will finish up with the Quotient rule and the Composite Rule. Once we have these two in place, I will continue with some examples so that you see differentiation in action.