How to find the slope of a straight line and its derivative ? What is the relation between the slope of a curve or a parabola and its derivative ? How to find the derivative of the composite of two functions f(g(x)), an exponential or trigonometric function, a logarithmic function,… ? 
1. Calculate the slope of a straight line and its derivative : Solution 1 

Given the graph of the following linear function :
and knowing that the equation of the straight line you are asked to :
a) find the slope of the straight line graphically with
b) figure out the derivative y ' of this straight line
c) conclude something on the obtained results 

2. Compute the slope of a curve and its derivative : Solution 2 

Given the graph and the quadratic equation of the
you are asked to :
a) find out the derivative y ' of the parabola equation
b) find out graphically the slope of the tangent line to
c) find the equation of that tangent line,
d) figure out the derivative of the tangent
e) reach a conclusion on the results obtained 

3. Compute the derivative of the following functions






































4. Derivate the following functions (derivative formulas) :











































Solution 4.22 Interesting ! 