Differential Calculus Calculators

Calculators for Derivatives

Derivatives (Up to the tenth derivative)

Use only $x$
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Determine the derivative of a function up to the tenth derivative
(2.) Graph the derivative of the function.

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed. Do not include $y = \;\;the\;\;function$
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the small textbox of the calculator.
(5.) Click the "Submit" button.
(6.) Check to make sure that it is the correct function you typed.
(7.) Review the answers. At least one of the answers is probably what you need.

Using the Derivatives Calculator
Type: $7$ as 7
Type: $4x + 3$ as 4 * x + 3 * x
Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
Type: $4x^3 - 5x^2 + 4$ as 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $|-7 - 5x|$ as |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $\sec^2 x$ as sec^2 x
Type: $\cos hx$ as cos hx
Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Differentiate $wrt\;x$

Applications of Derivatives

Extrema

Use only $x$
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Determine the extrema (maxima and minima) of a function within a domain.
(2.) Determine the extrema (maxima and minima) of a function without bounds. In this case, please specify the bounds are $-\infty$ and $\infty$.
(3.) Graph the function and indicate the extrema on the graph.

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed. Do not include $y = \;\;the\;\;function$
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the appropriate textbox of the calculator.
(5.) Type the domain of the function accordingly in the appropriate textbox of the calculator.
(6.) Click the Submit button.
(7.) Check to make sure that it is the correct function and domain that you typed.
(8.) Review the answers. At least one of the answers is probably what you need.

Using the Extrema Calculator
Type: $-\infty$ as -\infty
Type: $\infty$ as \infty
Type: $7$ as 7
Type: $4x + 3$ as 4 * x + 3 * x
Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
Type: $4x^3 - 5x^2 + 4$ as 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $|-7 - 5x|$ as |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $\sec^2 x$ as sec^2 x
Type: $\cos hx$ as cos hx
Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Function:

Stationary Points

Use only $x$

This calculator will:
(1.) Determine the stationary points on the function/curve
(3.) Specify if the stationary point is a maximum or minimum

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed. Do not include $y = \;\;the\;\;function$
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the appropriate textbox of the calculator.
(5.) Click the Submit button.
(6.) Check to make sure that it is the correct function that you typed.
(7.) Review the answers.

Using the Stationary Points Calculator
Type: $7$ as 7
Type: $4x + 3$ as 4 * x + 3 * x
Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
Type: $4x^3 - 5x^2 + 4$ as 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $|-7 - 5x|$ as |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $\sec^2 x$ as sec^2 x
Type: $\cos hx$ as cos hx
Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Function:

Optimization

Use only $x$ and $y$
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Determine the global/absolute extrema (global maximum and global minimum) and local/relative extrema (relative maximum and relative minimum) of a function (as applicable) within several constraints.
(2.) Graph three-dimensional plot (3D plot) and a contour plot of the objective funtion within the constraints.
(2.) Indicate the extrema on those plots.

To use the calculator, please:
(1.) Type the objective function in the first textbox (the bigger textbox).
(2.) Type it according to the examples I listed. Do not include $y = \;\;the\;\;function$
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the appropriate textbox of the calculator.
(5.) Type the constraints in the second textbox (the bigger textbox).
Separate each constraint with a comma. Do not put a comma or period at the end.
(6.) Copy and paste the constraints you typed, into the appropriate textbox of the calculator.
(7.) Click the Optimize button.
(8.) Check to make sure that it is the correct function and domain that you typed.
(9.) Review the answers. At least one of the answers is probably what you need.

Using the Optimization Calculator
Type: $-\infty$ as -\infty
Type: $\infty$ as \infty
Type: $7$ as 7
Type: $4x + 3$ as 4 * x + 3 * x
Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
Type: $4x^3 - 5x^2 + 4$ as 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $|-7 - 5x|$ as |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $\sec^2 x$ as sec^2 x
Type: $\cos hx$ as cos hx
Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Objective Function:

Constraints:

Newton's Method

Use only $x$

This calculator will:
(1.) Determine the derivative of the function.
(2.) Write the formula for Newton's method.
(3.) Lists all the iterations until a solution (zero of the function) is found.
(4.) Displays situations where Newton's method does not converge.

To use the calculator, please:
(1.) Type the function in the first textbox (big textbox).
(2.) Type it according to the examples I listed. Do not include $y = \;\;the\;\;function$
(3.) Delete the "default" function in the textbox of the calculator (the equation (ecuacion)).
(4.) Copy and paste the function you typed, into the first textbox of the calculator.
(5.) Type the value of the initial guess in the second textbox of the calculator.
(6.) Type the number of digits for each iteration results in the third textbox the calculator.
(7.) Click the Calcular (Calculate) button.
(8.) Check to make sure that the function you pasted is the actual function.
(9.) Review the answers.

Using the Newton's Method Calculator
Type: $4x + 3$ as 4 * x + 3 * x
Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
Type: $4x^3 - 5x^2 + 4$ as 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $|-7 - 5x|$ as |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $\sec^2 x$ as sec^2 x
Type: $\cos hx$ as cos hx
Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Function: