OEF Derivatives
--- Introduction ---
This module actually contains 35 exercises on derivatives of real
functions of one variable.
Arc and Arg
Establish the correspondence between the fucntions and their derivatives in the following table.
Circle
We have a circle whose radius increases at a constant speed of centimeters per second. At the moment when the radius equals centimeters, what is the speed at which its area increases (in
/s)?
Circle II
We have a circle whose radius increases at a constant speed of centimeters per second. At the moment when its area equals square centimeters, what is the speed at which the area increases (in
/s)?
Circle III
We have a circle whose area increases at a constant speed of square centimeters per second. At the moment when the area equals cm2, what is the speed at which its radius increases (in cm/s)?
Circle IV
We have a circle whose area increases at a constant speed of square centimeters per second. At the moment when its radius equals cm, what is the speed at which the radius increases (in cm/s)?
Composition I
We have two differentiable functions
and
, with values and derivatives shown in the following table. Let
be defined by
. Compute the derivative
.
Composition II *
We have 3 differentiable functions
,
and
, with values and derivatives shown in the following table. Let
the function defined by
. Compute the derivative
.
Mixed composition
We have a differentiable function
, with values and derivatives shown in the following table. Let
, and let
defined by
. Compute the derivative
.
Virtual chain Ia
Let
be a differentiable function, with derivative
. Compute the derivative of
.
Virtual chain Ib
Let
be a differentiable function, with derivative
. Compute the derivative of
.
Division I
We have two differentiable functions
and
, with values and derivatives shown in the following table. Let
defined by
. Compute the derivative
.
Mixed division
We have a differentiable function
, with values and derivatives shown in the following table. Let
defined by
. Compute the derivative
.
Hyperbolic functions I
Compute the derivative of the function
defined by
.
Hyperbolic functions II
Compute the derivative of the function
defined by
.
Multiplication I
We have two differentiable functions
and
, with values and derivatives shown in the following table. Let
. Compute the derivative
.
Multiplication II
We have two differentiable functions
and
, with values and derivatives shown in the following table. Let
. Compute the second derivative
.
Mixed multiplication
We have a differentiable function
, with values and derivatives shown in the following table. Let
defined by
. Compute the derivative
.
Virtual multiplication I
Let
be a differentiable function, with derivative
. Compute the derivative of
.
Polynomial I
Compute the derivative of the function
defined by
, for
.
Polynomial II
Compute the derivative of the function
defined by
.
Rational functions I
Compute the derivative of the function
Rational functions II
Compute the derivative of the function
Inverse derivative
Let
be the function defined by
.
Verify that
is bijective, therefore we have an inverse function
. Calculate the value of its derivative
at
. You must reply with a precision of at least 4 significant digits.
Rectangle I
We have a rectangle whose at a constant speed of centimeters per second, but whose stays constant at . At the moment when equals , what is the speed (in ) at which changes?
Rectangle II
We have a rectangle whose at a constant speed of centimeters per second, but whose stays constant at . At the moment when equals , what is the speed (in ) at which changes?
Rectangle III
We have a rectangle whose at a constant speed of centimeters per second, but whose stays constant at . At the moment when equals , what is the speed (in ) at which changes?
Rectangle IV
We have a rectangle whose at a constant speed of centimeters per second, but whose stays constant at . At the moment when equals , what is the speed (in ) at which changes?
Rectangle V
We have a rectangle whose at a constant speed of centimeters per second, but whose stays constant at . At the moment when equals , what is the speed (in ) at which changes?
Rectangle VI
We have a rectangle whose at a constant speed of centimeters per second, but whose stays constant at . At the moment when equals , what is the speed (in ) at which changes?
Right triangle
We have a right triangle as follows, where AB= , and AC at a constant speed of /s. At the moment when AC= , what is the speed at which BC changes (in /s)?
Sign of a number
Construct a study of the sign of
by choosing four of the sentences given below. - ,
- ,
- ,
- ,
Tower
Somebody walks towards a tower at a constant speed of meters per second. If the height of the tower is meters, at what speed (in m/s) does the distance between the man and the top of the tower decrease, when the distance between him and the foot of the tower is meters?
Trigonometric functions I
Compute the derivative of the function
defined by
.
Trigonometric functions II
Compute the derivative of the function
.
Trigonometric functions III
Compute the derivative of the function
defined by
at the point
.
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- Description: collection of exercises on derivatives of functions of one variable. interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: interactive mathematics, interactive math, server side interactivity, analysis, calculus, derivative, functions, limit