#
OEF derivatives
--- Introduction ---

This module actually contains 33 exercises on derivatives of real
functions of one variable.

### Circle

We have a circle whose radius increases at a constant speed of centimeters per second. At moment time when the radius equals centimeters, what is the speed at which its area increases (in cm^{2}/s)?

### Circle II

We have a circle whose radius increases at a constant speed of centimeters per second. At moment time when its area equals square centimeters, what is the speed at which the area increases (in cm^{2}/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 cm^{2}, 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 *f*(x) and *g*(x), with values and derivatives shown in the following table. x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |

*f*(x) | | | | | | | |

*f* '(x) | | | | | | | |

*g*(x) | | | | | | | |

*g*'(x) | | | | | | | |

Let *h*(x) = *f*(*g*(x)). Compute the derivative *h*'().

### Composition II *

We have 3 differentiable functions *f*(x), *g*(x) and *h*(x), with values and derivatives shown in the following table. x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |

*f*(x) | | | | | | | |

*f* '(x) | | | | | | | |

*g*(x) | | | | | | | |

*g*'(x) | | | | | | | |

*h*(x) | | | | | | | |

*h*'(x) | | | | | | | |

Let s(x) = *f*(*g*(*h*(x))). Compute the derivative s'().

### Mixed composition

We have a differentiable function *f*(x), with values and derivatives shown in the following table. Let *g*(x) = , and let *h*(x) = *g*(*f*(x)). Compute the derivative *h*'().

### 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 *f*(x) and *g*(x), with values and derivatives shown in the following table. x | -2 | -1 | 0 | 1 | 2 |

*f*(x) | | | | | |

*f* '(x) | | | | | |

*g*(x) | | | | | |

*g*'(x) | | | | | |

Let *h*(x) = *f*(x)/*g*(x). Compute the derivative *h*'().

### Mixed division

We have a differentiable function *f*(x), with values and derivatives shown in the following table. Let *h*(x) = / *f*(x). Compute the derivative *h*'().

### Hyperbolic functions I

Compute the derivative of the function *f*(x) = .

### Hyperbolic functions II

### Multiplication I

We have two differentiable functions *f*(x) and *g*(x), with values and derivatives shown in the following table. x | -2 | -1 | 0 | 1 | 2 |

*f*(x) | | | | | |

*f* '(x) | | | | | |

*g*(x) | | | | | |

*g*'(x) | | | | | |

Let *h*(x) = *f*(x)*g*(x). Compute the derivative *h*'().

### Multiplication II

We have two differentiable functions *f*(x) and *g*(x), with values and derivatives shown in the following table. x | -2 | -1 | 0 | 1 | 2 |

*f*(x) | | | | | |

*f* '(x) | | | | | |

*f* ''(x) | | | | | |

*g*(x) | | | | | |

*g*'(x) | | | | | |

*g*''(x) | | | | | |

Let *h*(x) = *f*(x)*g*(x). Compute the second derivative *h*''().

### Mixed multiplication

We have a differentiable function *f*(x), with values and derivatives shown in the following table. Let *h*(x) = *f*(x). Compute the derivative *h*'().

### Virtual multiplication I

Let
be a differentiable function, with derivative
. Compute the derivative of
.

### Polynomial I

Compute the derivative of the function *f*(x) = , for x=.

### Polynomial II

Compute the derivative of the function
.

### Rational functions I

### Rational functions II

### Inverse derivative

Let : -> be the function defined by (x) = . Verify that is bijective, therefore we have an inverse function (x) = ^{-1}(x). Calculate the value of derivative `'`() .

You must reply with a pricision 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)?

### Tower

Somebody walks towards a tower at a constant speed of meters per second. If the height of the tower is meters, at which speed (in m/s) the distance between the man and the top of the tower decreases, when the distance between him and the foot of the tower is meters?

### Trigonometric functions I

Compute the derivative of the function *f*(x) = .

### Trigonometric functions II

### Trigonometric functions III

Compute the derivative of the function *f*(x) = at the point x=.
Other exercises on:
derivatives
Calculus

**
This page is not in its usual appearance because WIMS is unable to recognize your
web browser.**

Please take note that WIMS pages are interactively generated; they are not ordinary
HTML files. They must be used interactively ONLINE. It is useless
for you to gather them through a robot program.

Description: collection of exercises on derivatives of functions of one variable. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: wims, mathematics, mathematical, math, maths, interactive mathematics, interactive math, interactive maths, mathematic, online, calculator, graphing, exercise, exercice, puzzle, calculus, K-12, algebra, mathématique, interactive, interactive mathematics, interactive mathematical, interactive math, interactive maths, mathematical education, enseignement mathématique, mathematics teaching, teaching mathematics, algebra, geometry, calculus, function, curve, surface, graphing, virtual class, virtual classes, virtual classroom, virtual classrooms, interactive documents, interactive document, analysis, calculus, derivative, function, limit