## Basic Math Level with Derivative Exercise and Answer Online

### 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).

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

Solution 4.22 Interesting !

The 18 derivative rules               Derivative exercises : intermediate level