Homework, Section 2.3

pp. 136--, #17, 21, 29, 41, 51
Andy Long

(* #17 *)
f[x_]:=(x^2+4x+3)/Sqrt[x]
Simplify[f'[x]]
Expand[f'[x]]

(* #21 *)
f[t_]:=t^(1/5)+4Sqrt[t^5];
Simplify[f'[t]]

(* #29 *)
g[x_]:=(1+2x)/(3-4x);
Simplify[g'[x]]

(* #41 *)
f[t_]:=t^(1/3)(t^2+t+t^(-1))
Simplify[f'[t]]
Expand[f'[t]]

(* #51 *)
y[x_]:=2x/(x+1);
Simplify[y'[x]]
T[x_]:=y'[1](x-1)+y[1]
T[x]
Plot[{y[x],T[x]},{x,0,2}]