Differentiation          03/24/16

 

Differentiation is by far the most important topic in a calculus course. Let’s turn the clock back. When you were in algebra, you were able to find the slope of a linear line that contained a rise over a run. Now, you were told that you were unable to find the slope for a line that was not constantly linear in nature. This is where calculus comes in. What you do is that you start out with your simple yxequation (y-y0x  →  f(x)-f(x0))x→ f(x0+x)-f(x0)x → f(x0+h)-f(x0)h ) and you evaluate it at smaller and smaller increments, until it becomes zero. Mathematically speaking, you are taking the limit as the change in x approaches zero, which can be symbolically analyzed as x0yx. We call this a derivative and we represent this concept with dydx, or the derivative of y in respect to x. Differentiation is a most useful way to find the instantaneous slope of tangent lines.