10 SCREEN 12
20 DEFDBL A-Z
30 PRINT "The Derivative By the Chain Rule"
40 PRINT "F'(x)=f(g(x))g'(x)"
50 PRINT "If y=f(u),u=g(x) then (dy/dx)=(dy/du)*(du/dx)"
70 PRINT "Example: f(x)="; CHR$(251); "(1+x^2); x=2"
80 PRINT "Substituting u for 1+x^2 f(u)=u^(1/2)"
90 PRINT "f'(u)=(1/2)*u^(-1/2)"
100 PRINT "(du/dx)=2x"
110 PRINT "(dy/du)=(1/2)*1/"; CHR$(251); "(1+x^2)"
120 PRINT "f'(x)=(dy/dx)=(dy/du)*(du/dx)=x/"; CHR$(251); "(1+x^2)"
130 a = 2 / (1 + (2 ^ 2)) ^ (1 / 2)
140 PRINT "if x=2 then f'(x)=2/(1+(2^2))^(1/2)="; a
150 SYSTEM