Derivatives: Addition & Subtraction

This post will elaborate more on the basics of derivatives.  As you may recall, we discussed in the previous post that the derivative of axⁿ, a being any constant, is (n*a)x^n-1.  When dealing with a larger function, this rule still applies.  Consider this example:

f(x) = 3x⁴ + 2x + 18

We have learned how to find the derivative of these individually, but what would you do if there are lots of these added together?  Quite simple, actually.  You take the derivative of each addend individually.  So for the solution to the above problem:

f '(x) = (4*3)x^4-1 + (1*2)x^1-1 + 0
f '(x) = 12x³ + 2

As you can see, these will give you no problem as long as you are familiar with the simple derivatives.  The same approach is taken for subtraction.  Here is an example:

f(x) = 4x³ - 8x - 8
f '(x) = (3*4)x^3-1 - (1*8)x^1-1 - 0
f '(x) = 12x² - 8

Again, very simple.  Since the rule applied to both is the exact same, you could very easily differentiate a function that included both addition and subtraction.  Just to be clear, I will list another example.

f(x) = 5x² - x + 4
f '(x) = (2*5)x^2-1 - (1*1)x^1-1 + 0
f '(x) = 10x - 1

This concludes addition and subtraction using differentiation.  We will get into multiplication and division in later posts, but it is slightly more complex.  In the next tutorial we will cover how to take multiple derivatives of the same function.  Hope this was helpful and stay tuned!