This tool calculates the nth derivative of any mathematical function you input.

nth Derivative Calculator

Use this calculator to find the nth derivative of a polynomial function with respect to a variable.

How to Use

1. Enter the polynomial function in the Function f(x) field. For example: x^3 + 2*x^2 - x + 1
2. The variable is set to x and cannot be changed.
3. Enter the order of the derivative you want to compute in the Derivative order (n) field. For example, for the first derivative, enter 1
4. Click the Calculate button to see the result in the Result field.

How it Calculates

The calculator uses basic differentiation rules for polynomials. It parses the polynomial function, differentiates term by term, and then constructs the resultant polynomial after computing the nth derivative.

Limitations

This calculator currently handles only polynomial functions. It does not support trigonometric, exponential, logarithmic, or other non-polynomial functions. The variable is fixed to x, and input functions must be entered in the format ax^n + bx^(n-1) + ... + c where each term is either a constant or a mono-variable raised to an integer power.

Use Cases for This Calculator

Calculating the 1st Derivative

Enter an equation and specify the variable to find the 1st derivative effortlessly. The calculator will compute the derivative using the power rule, product rule, quotient rule, or chain rule as needed.

Calculating the 2nd Derivative

After finding the 1st derivative, easily click a button to find the 2nd derivative without re-entering the equation. It simplifies the process by recursively applying the derivative rules.

Calculating Higher Order Derivatives

Continue finding successive derivatives by selecting the order you desire. The calculator will iteratively calculate the higher order derivatives, providing a quick solution for complex calculus problems.

Applying Chain Rule for Derivatives

When dealing with composite functions, simply input the function and the inner function to automatically apply the chain rule. The calculator handles the chain rule intricacies, saving you time and effort.

Handling Trigonometric Functions

Effortlessly differentiate trigonometric functions like sine, cosine, and tangent by inputting the function. The calculator understands trigonometric rules to derive these functions accurately.

Dealing with Exponential Functions

Input exponential functions like e^x or any base exponentiation to get the derivative calculated promptly. The calculator efficiently processes exponential rules to provide precise results.

Handling Logarithmic Functions

Input logarithmic functions like ln(x) or log(x) with any base to compute their derivatives with ease. The calculator handles logarithmic rules for differentiation effortlessly.

Verifying Derivatives of Custom Equations

Input custom equations to verify derivatives step by step. The calculator shows each derivative calculation, aiding in understanding the differentiation process better.

Swiftly Checking Derivatives’ Accuracy

Verify the accuracy of the calculated derivatives by checking against manual derivations. The calculator helps in quick validation of derivative results for confidence in your calculus work.

Effortlessly Differentiating Implicit Equations

Input implicit equations, including x and y variables, to differentiate implicitly without complex manual steps. The calculator handles implicit differentiation seamlessly, simplifying implicit calculus problems.