Week 6

This week we continued to learn about derivatives and how they work. We learned about graphing the derivative and what the graph means. When the graph of the derivative is below the x-axis then that means that the original graph is decreasing. When the derivative is above the x-axis the original function is increasing. The zeros of the derivative graph are the maxima and minima of the original graph. This I a concept that I grasped pretty well. After looking at multiple examples it really made sense to me. We also learned about other ways to denote a derivative. The most common is dy/dx which reads "the derivative of y with respect to x." Also there is d/dx which reads "the derivative of f at x." Next we learned about where a derivative fails to exist. Those places are corners, cusps, vertical tangent, and discontinuities. This was a good thing to know because on the quiz there was a question that dealt with several of these things. Next we learned a shortcut to finding the derivative which would have been helpful when we first started learning about derivatives. The short cut is this... f(x)=x^n then f'(x)=xn^(n-1). That makes it really simple to quickly find the derivative of any function. Also we learned about the nderive feature on the calculator. This makes it easy to graph a derivative or find the derivative at a point. Then we took a quiz which I got a 28.5/30 so I was pretty happy. Today we learned about the product and quotient rules for derivatives. So far those don't really make much sense but I haven't had any practice with them yet so I'm sure they will make sense soon. The product rule reads... d/dx(u•v)=dv/dx(u)+du/dx(v). The quotient rule reads... d/dx (u/v)=( du/dx(v)-dv/dx(u))/v^2. That one is pretty complicated and doesn't make much sense yet. Finally we learned about higher order derivatives which is basically just taking the derivative of a derivative. It's pretty easy. Overall this was a pretty productive week I would say.