var('x,y,z')
f=x^2*y+y^2
print("1)")
print("fx",diff(f,x))
print("fy",diff(f,y))
print("2)")
print("fxx",diff(diff(f,x),x))
print("fxy",diff(diff(f,x),y))
print("fyy",diff(diff(f,y),y))
print("fyx",diff(diff(f,y),x))
f=(e^x)*cos(y)
print("3)")
print("fx",diff(f,x))
print("fy",diff(f,y))
print("fxx",diff(diff(f,x),x))
print("fxy",diff(diff(f,x),y))
print("fyy",diff(diff(f,y),y))
print("fyx",diff(diff(f,y),x))
print("4)")
fx=diff(f,x)
fy=diff(f,y)
fxv=fx(0,0)
fyv=fy(0,0)
plane=fxv*(x-0)+fyv*(y-0)+1
print(plane)
print("5)")
a=implicit_plot3d((e^x)*cos(y)==z,(x,-10,10),(y,-10,10),(z,-10,10))
b=implicit_plot3d(plane==z,(x,-10,10),(y,-10,10),(z,-10,10),color='red')
print("6)")
print(plane(.1))
f=x*y^2-x^3+10
print("7)")
print("fx",diff(f,x))
print("fy",diff(f,y))
print("fxx",diff(diff(f,x),x))
print("fxy",diff(diff(f,x),y))
print("fyy",diff(diff(f,y),y))
print("fyx",diff(diff(f,y),x))
print("8)")
fx=diff(f,x)
fy=diff(f,y)
fxv=fx(1,1.5)
fyv=fy(1,1.5)
plane2=fxv*(x-1)+fyv*(y-1.5)+11.25
print(plane2)
print("9)")
c=implicit_plot3d(x*y^2-x^3+10
==z,(x,-10,10),(y,-10,10),(z,-10,10))
d=implicit_plot3d(plane2==z,(x,-10,10),(y,-10,10),(z,-10,10),color='red')
print("10)")
print(plane2(1.1,1.2))
c+d
