CASIO

Derivative(d/dx) obtains the approximate differential coefficient at the specified x-coordinate (a) in the input f(x) expression.

Input Syntax

The input syntax depends on the Input/Output setting on the SETTINGS menu, as shown in the table below.

* tol specifies tolerance, which becomes 1 × 10-16 when nothing is input for tol.

Derivative Calculation Precautions

When using a trigonometric function in f(x), specify "Radian" as Angle Unit on the SETTINGS menu.

A smaller tol value increases precision, but it also increases calculation time. When specifying tol, use a value that is 1 × 10-22 or greater.

Inaccurate results and errors can be caused by the following:

Derivative Calculation Example

Determine f’(^π₂) when f(x) = sin(x) (tol specification omitted.)

(Input/Output: MathI/MathO, Angle Unit: Radian)

• – [Func Analysis] > [Derivative(d/dx)]
  (π)2
• 

(Input/Output: LineI/LineO, Angle Unit: Radian)

• – [Func Analysis] > [Derivative(d/dx)]
  (,)(π)2
• 

This calculator performs integration using the Gauss-Kronrod method of numerical integration.

Input Syntax

The input syntax depends on the Input/Output setting on the SETTINGS menu, as shown in the table below.

* tol specifies tolerance, which becomes 1 × 10-10 when nothing is input for tol.

Integration Calculation Precautions

When using a trigonometric function in f(x), specify "Radian" as Angle Unit on the SETTINGS menu.

A smaller tol value increases precision, but it also increases calculation time. When specifying tol, use a value that is 1 × 10-22 or greater.

Depending on the content of f(x), positive and negative values within the region of integration or the region of integration, large error may result in calculated integration values. (Examples: When there are parts with discontinuous points or abrupt change. When the integration interval is too wide.) In such cases, dividing the integration interval into multiple parts and then performing calculations may improve calculation accuracy.

Integration Calculation Example

(ln(x), 1, e) = 1 (tol specification omitted.)

(Input/Output: MathI/MathO)

• – [Func Analysis] > [Integration(∫)]
  (ln)1(e)
• 

(Input/Output: LineI/LineO)

• – [Func Analysis] > [Integration(∫)]
  (ln)(,)1(,)(e)
  
• 

With Σ(, you can obtain the sum of an input f(x) expression for a specific range.

Input Syntax

The input syntax depends on the Input/Output setting on the SETTINGS menu, as shown in the table below.

* a and b are integers that can be specified within the range of -1 × 1010 < a ≤ b < 1 × 1010.

Σ Calculation Example

(x + 1) = 20

(Input/Output: MathI/MathO)

• – [Func Analysis] > [Summation(Σ)]
  115
• 

(Input/Output: LineI/LineO)

• – [Func Analysis] > [Summation(Σ)]
  1(,)1(,)5
• 

Use (log) or – [Func Analysis] > [Logarithm(log)] to input logab as log (a, b). Base 10 is the initial default setting if you do not input anything for a.

Example 1: log101000 = log 1000 = 3

• (log)1000
• 

Example 2: log216 = 4

• (log)2(,)16
• 

The key (or – [Func Analysis] > [Logarithm(logab)]) also can be used for input, but only while MathI/MathO or MathI/DecimalO is selected for Input/Output on the SETTINGS menu. In this case, you must input a value for the base.

Example 3: log216 = 4

• 216
• 

Use (ln) or – [Func Analysis] > [Natural Logarithm] to input "ln".

Example: ln 90 (= loge90) = 4.49980967

• (ln)90
•