# Homework # 7
# Selected Answers
# 
> restart:
# Question 1:
> f:=4*x^3*y^2+3*x^2*y^4-7*x*y^2+4*x-3*y+2;
> fx=diff(f,x);
> fy=diff(f,y);
# Question 2:
> f:=x^3*exp(2*y)+y^2*ln(3*x);
> fx=diff(f,x);
> fy=diff(f,y);
# Question 3:
> f:=(5*x*y^2)/(x^3+y^3);
> fx=diff(f,x);
> fy=diff(f,y);
# Question 4:
> f:=4*y^3/(x^3+y^2);
> fx=diff(f,x);
> fy=diff(f,y);
# Question 5:
> f:=x^2*sqrt(y^2+z);
> fx=diff(f,x);
> fy=diff(f,y);
> fz=diff(f,z);
# Question 6:
> f:=x^2*y*z^2+x*y^2*z+x*y;
> fx:=diff(f,x);
> fx_solution=subs({x=1,y=2,z=3},fx);
# Question 7
> z:=exp(x/y);
> fy=diff(z,y);
# Question 8:
> Q:=sqrt((2*C*M)/s);
> Qc:=diff(Q,C);
> solution=subs({C=100,M=500,s=3},Qc);
> evalf(%);
# Question 9:
> c:=0.002*(x+y)^2+x+0.25*y+8000;
> Cx:=diff(c,x);
> subs({x=450,y=550},Cx);
> restart:
# Question 10
> p:=2.1*L^(0.6)*K^(0.4);
> MP_labour:=diff(p,L);
> MP_capital:=diff(p,K);
>