Lecture 6

1. Calculate the first derivatives of the following functions:

                                                                                                 a)

b)

c)

d)


2. Calculate the derivative of the function at the given point:

                                                                                                 a)

b)

c)

d)


3. Calculate the derivative of the product of two functions

                                                                                                 a)

b)

c)

d)

e)


4. Calculate:

                                                                                                 a)

b)

c)

d)


5. Derivate composite function:

In simple words, we say that the derivative of a composite function is the product of the
derivative of the outside function with respect to the inside function and the derivative of the
inside function with respect to the variable.

                                                                                                 a)

b)

c)

d)


The derivative of a function y = f(x) of a variable x is a measure of the rate at which the value y
of the function changes with respect to the change of the variable x. It is called the derivative
of f with respect to x.

The second derivative is the rate of change of the rate of change of a point at a graph (the "slope
of the slope" if you will). This can be used to find the acceleration of an object (velocity is
given by first derivative).

If a function f´(x) can be differentiated, we obtain the second derivative of f(x), denoted as
f´´(x), and so on.


6. Calculate the first, second and third derivatives of the functions:

                                                                                                 a)

b)

c)

d)