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
        shown is

        you are asked to :

        a) find the slope of the straight line graphically with
        the help of the formula : slope = ΔY / ΔX ,

        b) figure out the derivative y ' of this straight line
        equation with the help of the derivative rules,

        c) conclude something on the obtained results
        in a) and b).

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

        Given the graph and the quadratic equation of the
        following parabola y = x² + 1 and its tangent line
        at x = -2,

        you are asked to :

        a) find out the derivative y ' of the parabola equation
        with the help of the derivative formulas,

        b) find out graphically the slope of the tangent line to
        the parabola at x = -2, with the help of the formula
        slope = ΔY / ΔX ,

        c) find the equation of that tangent line,

        d) figure out the derivative of the tangent
        line equation with the help of the derivative
        formulas,

        e) reach a conclusion on the results obtained
        in b) and d).

3. Compute the derivative of the following functions
    (use the derivative rules)

Solution 3.1

Solution 3.2

Solution 3.3

Solution 3.4

Solution 3.5

Solution 3.6

Solution 3.7

Solution 3.8

Solution 3.9

Solution 3.10

Solution 3.11

Solution 3.12

Solution 3.13

Solution 3.14

Solution 3.15

Solution 3.16

Solution 3.17

Solution 3.18

4. Derivate the following functions (derivative formulas) :
    composite of two functions f(g(x), exponential, logarithmic function,
    trigonometric function,...

Solution 4.1

Solution 4.2

Solution 4.3

Solution 4.4

Solution 4.5

Solution 4.6

Solution 4.7

Solution 4.8

Solution 4.9

Solution 4.10

Solution 4.11

Solution 4.12

Solution 4.13

Solution 4.14

Solution 4.15

Solution 4.16

Solution 4.17

Solution 4.18

Solution 4.19

Solution 4.20

Solution 4.21

Solution 4.22 Interesting !