feat: chain rule

src/main.py

@@ -1,8 +1,10 @@
 from sympy import diff, limit, oo, symbols
 
 from modules.math import (
-    t_build_partial_derivate,
 	t_build_derivate,
+	t_build_derivative_from_limit,
+	t_build_partial_derivate,
+	t_calculate_derivative_limit,
 	t_calculate_e,
 	t_calculate_e_limit,
 	t_compound_interest,
@@ -37,4 +39,17 @@ if __name__=="__main__":
 	partial_derivative_y = t_build_partial_derivate((3 * y ** 3) + 2 * z ** 2, y)
 	partial_derivative_z = t_build_partial_derivate((3 * y ** 3) + 2 * z ** 2, z)
 	print(partial_derivative_y, partial_derivative_z)
+	print(t_build_derivative_from_limit(x ** 2))
+	print(t_calculate_derivative_limit(x ** 2, 2))
 
+	## Chain rule
+	# for a given function y (lets say y = x ** 2 + 1) and another z (lets say z = y ** 3 - 2), we can find a derivativeof z with respect to x by multiplying the derivatives
+	# normal derivative calc
+	x = symbols("x")
+	z = (x ** 2 + 1) ** 3 - 2
+	print(t_build_derivate(z))
+	# chain rule calc
+	x, y, z = symbols("x y z")
+	y_f = x ** 2 + 1
+	z_f = y ** 3 - 2
+	print(t_build_derivate(y_f), t_build_derivate(z_f))

src/modules/math.py

@@ -55,6 +55,17 @@ def t_calculate_e_limit():
 def t_calculate_derivative(f, x, step_size):
 	return (f(x + step_size) - f(x)) / (x +step_size - x)
 
+def t_build_derivative_from_limit(f):
+	x, s = symbols("x s")
+	slope_f = (f.subs(x, x + s) - f) / (x + s - x) # Slope function
+	return limit(slope_f, s, 0)
+
+def t_calculate_derivative_limit(f, x_target):
+	x = symbols("x")
+	slope_f = t_build_derivative_from_limit(f)
+	return slope_f.subs(x, x_target)
+
+
 def t_build_derivate(f):
 	return diff(f)