Differentiation Calculator

Step-by-Step Guide to Using the Differentiation Calculator

Step 1: Select the Function Type

Begin by selecting the type of function you want to differentiate. This can be done using the dropdown menu labeled Select Function Type. You have four options to choose from:

• Polynomial (e.g., ax^n)
• Trigonometric (e.g., sin x, cos x)
• Exponential (e.g., e^x)
• Logarithmic (e.g., ln x)

Step 2: Enter the Coefficient

In the field labeled Coefficient (a), input the numerical value of the coefficient in your function. The input should be within the range of -1000 to 1000. Use increments of 0.1 to achieve the required precision.

Step 3: Provide the Power of x

If you selected Polynomial in the first step, you will need to specify the power, n, in the field labeled Power (n). Input a whole number value that ranges from -10 to 10.

Step 4: Input the Value of x for Evaluation

Enter the x value at which you wish to evaluate the derivative in the field labeled x Value. Acceptable values range from -100 to 100, with both integers and decimals (in steps of 0.1) being valid.

Step 5: View the Derivative Formula

Once you have filled out all the necessary input fields, the calculator will display the derivative formula in the Derivative Formula section. The calculator intelligently formats the formula based on your function type selection.

Step 6: Evaluate the Derivative at the Given x Value

The Derivative Value at x section will show the calculated value of the derivative at your specified x value. The result is formatted to four decimal places to provide a precise result suitable for analysis.

Step 7: Determine the Slope at the Point

The calculated value from the Derivative Value at x is directly used to determine the slope of the function at the given point. In the Slope at Point section, this value is displayed again with a suffix indicating the units per x, helping to contextualize the result.