Chapters

Calculate the Differential of the Following Functions:
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Solution of exercise 1
Solution of exercise 2
Solution of exercise 3
Solution of exercise 4
Solution of exercise 5
Solution of exercise 6
Solution of exercise 7
Solution of exercise 8

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Calculate the Differential of the Following Functions:

Exercise 1

$\text{[math]}$

Exercise 2

$\text{[math]}$

Exercise 3

$\text{[math]}$

Exercise 4

$\text{[math]}$

Exercise 5

A square has a side of 2 m. Determine the increase in area of the square when its sides increase by 1 milimeter. Calculate the error made when using differentials rather than increases.

Exercise 6

Find the change in the volume of a cube of with edges of 20 centimeters, when each edge increases by 0.2 cm in length..

Exercise 7

Calculate the absolute and relative error made when calculating the volume of a sphere of 12.51 milimeters in diameter, measured with an instrument that shows thousandths of a centimeter.

Exercise 8

If $\text{[math]}$ is replaced by $\text{[math]}$ , what are the approximations of absolute and relative error?

Solution of exercise 1

Calculate the differential:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 2

Calculate the differential:

$\text{[math]}$ $\text{[math]}$

Solution of exercise 3

Calculate the differential:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 4

Calculate the differential:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 5

A square has a side of 2 m. Determine the increase in area of the square when its sides increase by 1 milimeter. Calculate the error made when using differentials rather than increases.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Error = $\text{[math]}$

Solution of exercise 6

Find the change in the volume of a cube of with edges of 20 centimeters, when each edge increases by 0.2 cm in length.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 7

Calculate the absolute and relative error made when calculating the volume of a sphere of 12.51 milimeters in diameter, measured with an instrument that shows thousandths of centimeter.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 8

If $\text{[math]}$ is replaced by $\text{[math]}$ , what are the approximations of absolute and relative error?

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

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Differential Problems

Calculate the Differential of the Following Functions:

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Solution of exercise 1

Solution of exercise 2

Solution of exercise 3

Solution of exercise 4

Solution of exercise 5

Solution of exercise 6

Solution of exercise 7

Solution of exercise 8

Theory

Geometric Interpretation of the Derivative

Exponential Derivative

nth Derivative

Derivative

Basic Derivatives

Rate of Change

Derivatives

Derivatives of Trigonometric Functions

Inverse Function Rule

Physical Interpretation of the Derivative

Functional Power Rule

One-Sided Derivative

Derivative of an Implicit Function

Derivative Rules

Logarithmic Derivative

Derivatives of Inverse Trigonometric Functions

Chain Rule

Differentials

Equation of the tangent line

Differentiability and Continuity

Product and Quotient Rules

Derivative Function

Physics Derivative Problems and Worked Solutions

Formulas

Derivative Formulas

Calculus Formulas

Exercises

Tangent Problems

Calculus Problems and Worksheets

Derivative Problems

Derivatives Worksheet

Differential Problems

Derivatives Worksheet

Derivatives Worksheet II

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