3.1 & 3.2 Derivative formulas for powers and polynomials & exponential and logarithmic functions

Main points:
• Derivative of
○ Constant function is 0
○ Linear function is slope=m (when f(x)=b+mx)
○ Constant times a function is (d/dx)[cf(x)]=cf'(x) (when c is a constant)
○ Sum is (d/dx)[f(x)+g(x)]=f'(x)+g'(x)
○ Difference is (d/dx)[f(x)-g(x)]=f '(x)+g'(x)
• The power rule: (d/dx)(x^n)=nx^(n-1)
• (d/dx)(e^x)=e^x
• Exponential rule: (d/dx)(a^x)=(lna)a^x
• (d/dx)(lnx)=1/x

Challenges:
As going through the examples I found myself making careless mistakes such as putting unnecessary negative sign when differentiating √x. I definitely need to be careful as I am finding myself pretty comfortable with the differentiation in order to avoid simple mistakes. I am also from time to time getting confused with the graphs of function and their derivatives, especially when they are on the same graph. So spending more time with graphing would not be bad idea.

Reflection:
There was no examples related to economics which was something that I did not like, but luckily there are questions related to economics in the problem section. I was surprised how easily I remembered differentiation, but regardless that I was capable of using the rules I could not provide the correct notations for my work, just the answer to the differentiation. I know that differentiation is used many ways in social sciences and I am hoping to see more of its practical applications to the real world problems.