Derivatives
por Chanler May
1. Algebraic Deffintion
1.1. Finding the derivative by the limit process
1.2. f'x)=lim as h-->0 (f(x+h)-f(x)/h
1.3. Using the derivative to find the slope at a point
1.4. First find f'(x) and then use the given point to solve for slope.
2. Graphical Deffiniton
2.1. From viewing a graph you can determine a derivative.
2.2. Sharp turns indicate a derivative does not exist at that point.
3. Notation
3.1. f'(x)= lim as h-->0 f(x+h)-f(x)/h
3.2. f'(x)
3.3. dy/dx
3.4. d/dx[f(x)]
4. Special Rules
4.1. (d/dx)[cosx]=-sinx
4.2. (d/dx)[sinx]=cosx
4.3. (d/dx)[e^x]=e^x
5. Rules
5.1. The derivative only exist provided that the limit exist.
5.2. For all x values for which the limit exist f' is a function of x.
5.3. Constant Rule
5.3.1. (d/dx) [c]=0
5.4. Power Rule
5.4.1. (d/dx)[x^n] =nx^n-1
5.5. Constant Multiple Rule
5.5.1. (d/dx)[cf(x)]=cf'(x)
5.6. Sum and Difference Rule
5.6.1. (d/dx)[f(x)+or-g(x)]=f'(x)+or-g'(x)
6. Applications
6.1. How fast a colonies population will grow at a certain amount of time.
6.1.1. Using the exponential rule.
6.2. Rate of change of a moving ball.
6.2.1. Power Rule