# Calculate Derivative Functions in Java

Fellow coders, in this tutorial we are going to learn how to calculate the derivative of a function in Java. As we all know that, the derivative of a function measures the change in the output value with respect to the change in its input value.

## The derivative of a function in Java

Let us take a look at the function below:

**y = f(x)**

The derivative of the function above is the measure of the rate at which the value y of the above function changes with respect to the change of variable x. So, this is called a derivative of *f* with respect to *x*.

#### Working with the code:

We will calculate and print the derivative of:

**a x^2 + b x + c**

abstract class Expr { public abstract Expr d(String v); public Expr plus(Expr e2) { return new Plus(this, e2); } public Expr times(Expr e2) { return new Times(this, e2); } } class Int extends Expr { private final int n; public Int(int m) { n = m; } public Expr d(String v) { return new Int(0); } public String toString() { return Integer.toString(n); } } class Var extends Expr { private final String var; public Var(String v) { var = v; } public Expr d(String v) { return new Int(var.equals(v) ? 1 : 0); } public String toString() { return var; } } class Plus extends Expr { private final Expr e1, e2; public Plus(Expr a, Expr b) { e1 = a; e2 = b; } public Expr d(String v) { return new Plus(e1.d(v), e2.d(v)); } public String toString() { return "(" + e1 + " + " + e2 + ")"; } } class Times extends Expr { private final Expr e1, e2; public Times(Expr a, Expr b) { e1 = a; e2 = b; } public Expr d(String v) { return new Plus(new Times(e1, e2.d(v)), new Times(e1.d(v), e2)); } public String toString() { return "(" + e1 + " * " + e2 + ")"; } } public class derivative { public static void main(String[] args) { Expr x = new Var("x"), a = new Var("a"), b = new Var("b"), c = new Var("c"); Expr e = a.times(x).times(x).plus(b.times(x)).plus(c); System.out.println("d(" + e + ", x) = " + e.d("x")); } }

The output of the above code is:

d(((((a * x) * x) + (b * x)) + c), x) = (((((a * x) * 1) + (((a * 1) + (0 * x)) * x)) + ((b * 1) + (0 * x))) + 0)

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