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);