Chain Rule Calculator

How to Use the Chain Rule Calculator

This step-by-step guide will help you navigate through the Chain Rule Calculator to find the derivative using the chain rule. Follow the steps carefully to ensure accurate results.

Step 1: Select the Function Type

• Locate the drop-down menu labeled Select Function Type.
• Choose from the available options:
  • Power Rule: [u(x)]^n
  • Exponential: e^[u(x)]
  • Logarithmic: ln[u(x)]
  • Trigonometric: sin[u(x)]
• This selection determines the type of the outer function.

Step 2: Select the Inner Function

• Locate the drop-down menu labeled Select Inner Function u(x).
• Select one of the available inner function templates:
  • Linear: ax + b
  • Quadratic: ax² + bx + c
  • Cubic: ax³ + bx² + cx + d
• This choice will specify the inner function u(x) for the chain rule.

Step 3: Enter the Coefficients

• Provide the necessary coefficients for the selected inner function. Ensure each input meets the required step increment of 0.1:
  • Coefficient a: Required
  • Coefficient b: Required
  • Coefficient c: Optional, depends on the chosen inner function
  • Coefficient d: Optional, depends on the chosen inner function
• New forms will prompt you based on chosen function complexity.

Step 4: Enter the Exponent (if applicable)

• If you chose the Power Rule in step 1, enter the value for the exponent (n).
  • Ensure the exponent is entered as a whole number.
• This step is only necessary if you have selected the power function type.

Step 5: Calculate and Interpret the Results

• After entering all necessary inputs, the calculator will automatically compute the derivatives.
• The key results you will see include:
  • Outer Function Derivative: The derivative of the selected outer function, formatted to two decimal places.
  • Inner Function Derivative: The derivative of your chosen inner function, also formatted to two decimal places.
  • Final Derivative (Chain Rule Result): The final outcome of the chain rule application, expressed as a precise two-decimal value.

This completes the step-by-step instructions for using the Chain Rule Calculator. Make sure each input aligns with the specific rules associated with each function type to obtain a correct derivative.