Differential Calculator

Step-by-Step Guide to Using the Differential Calculator

This guide will walk you through using the Differential Calculator to derive and evaluate the slope of different mathematical functions at a specific point. Follow each step to input the necessary details, calculate derivatives, and understand the slope at a given point.

Step 1: Select the Function Type

• Locate the Function Type dropdown menu. Here, you need to specify the type of function you are analyzing.
• Select one of the following options:
  • Polynomial (e.g., x², x³)
  • Trigonometric (e.g., sin, cos, tan)
  • Exponential (e.g., e^x)
  • Logarithmic (ln x)

Step 2: Input the Coefficient

• In the Coefficient field, enter the coefficient for your function. For example, enter “2” for 2x².
• The value must be between -1000 and 1000, and you can use increments of 0.01.

Step 3: Enter the Power/Exponent

• In the Power/Exponent field, enter the power of the polynomial or the exponent for other function types.
• Enter an integer between 0 and 10. For instance, enter “2” for x².

Step 4: Specify the x Value

• Enter the x Value where you want to evaluate the derivative.
• This should be a number between -1000 and 1000, and accurate to two decimal places.

Step 5: Calculate the Derivative

Once you have entered all inputs, the calculator will automatically compute the derivative formula based on your inputs:

• For Polynomial functions, it uses the power rule to calculate the derivative.
• For Trigonometric functions, it derives to the respective trigonometric function with a coefficient.
• For Exponential functions, it retains the same exponential form multiplied by the coefficient.
• For Logarithmic functions, it calculates the derivative as the coefficient divided by x.

Step 6: Evaluate the Derivative at the Specified x Value

The calculator will also evaluate the derivative at the x Value you specified in Step 4. This gives the numerical value of the derivative at that point.

Step 7: Determine the Slope at the Point

The slope at the point is the value of the derivative at the specified x value. The calculator will display this in the output section.

With these steps, you can effectively use the Differential Calculator to analyze the behavior of different functions and their slopes at specified points.