Homework, Section 2.6: pp. 161--
Calculus I
Andy Long

#32, p. 164

Solve[D[y[x]^2(y[x]^2-4)-x^2(x^2-5),x]==0,y'[x]]

#55, p. 164

Clear[a,b,n,P,V]
{a,b,n,P,V}
soln=Solve[D[(P+n ^2a/(V[P]^2))*(V[P]-n b),P]==0,V'[P]]
exp=V'[P]/.First[First[soln]]
a=3.592
n=1
b=.04267
P=2.5
V[P]=10
{a,b,n,P,V[P]}
exp

#59, p. 164

soln=Solve[D[x^2y[x]^2+x y[x],x]==0,y'[x]]
exp=y'[x]/.First[First[soln]]
Solve[exp==-1,y[x]]
y[x_]:=x
Solve[x^2y[x]^2+x y[x]==2,x]