docs: Added documentation for nth_derivative function

CONTRIBUTORS.md

@@ -1,10 +0,0 @@
-## Contributors
-
-<!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->
-<!-- prettier-ignore-start -->
-<!-- markdownlint-disable -->
-[![All Contributors](https://img.shields.io/github/all-contributors/jono-rams/PolySolve?color=ee8449&style=flat-square)](#contributors)
-<!-- markdownlint-restore -->
-<!-- prettier-ignore-end -->
-
-<!-- ALL-CONTRIBUTORS-LIST:END -->

README.md

@@ -56,17 +56,22 @@ print(f"Value of f1 at x=5 is: {y_val}")
 # > Value of f1 at x=5 is: 30.0
 
 # 3. Get the derivative: 4x - 3
-df1 = f1.differential()
+df1 = f1.derivative()
 print(f"Derivative of f1: {df1}")
 # > Derivative of f1: 4x - 3
 
-# 4. Find roots analytically using the quadratic formula
+# 4. Get the 2nd derivative: 4
+df1 = f1.nth_derivative(2)
+print(f"2nd Derivative of f1: {df1}")
+# > Derivative of f1: 4
+
+# 5. Find roots analytically using the quadratic formula
 #    This is exact and fast for degree-2 polynomials.
 roots_analytic = quadratic_solve(f1)
 print(f"Analytic roots: {sorted(roots_analytic)}")
 # > Analytic roots: [-1.0, 2.5]
 
-# 5. Find roots with the genetic algorithm (CPU)
+# 6. Find roots with the genetic algorithm (CPU)
 #    This can solve polynomials of any degree.
 ga_opts = GA_Options(num_of_generations=20)
 roots_ga = f1.get_real_roots(ga_opts, use_cuda=False)

src/polysolve/__init__.py

@@ -488,6 +488,10 @@ if __name__ == '__main__':
     df1 = f1.derivative()
     print(f"Derivative of f1: {df1}")
 
+    # Find the second derivative: 4
+    ddf1 = f1.nth_derivative(2)
+    print(f"Second derivative of f1: {ddf1}")
+
     # --- Root Finding ---
     # 1. Analytical solution for quadratic
     roots_analytic = quadratic_solve(f1)