Mathematica Giving Me Trouble I'm new to mathematica and am just learning the basics.  I've run into a few things that I can't figure out.
The first is this:
"Number 11"

$$r[t\_] := \{(1/3)*(t^3), 0.5 * t^2, t\}$$

(*Unit Tangent Vector = $r'/\text{Length}(r')$ *)

$$ta = \frac{r'[t]}{\text{Norm}[r'[t]]}$$

(* Unit Normal Vector = $ta'$/Length($ta'$) *)

$$n = \frac{ta'[t]}{\text{Norm}[ta'[t]]}$$

(* Curvature = Length($ta'$)/Length($r'[t]$) *)

$$c = \frac{Norm[ta'[t]]}{\text{Norm}[r'[t]]}$$

"Number 11"

$$\{t^2/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4], (1. t)/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4], 1/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4]\}$$

.

Derivative[
    1][{t^2/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4], (1. t)/Sqrt[
     1 + 1. Abs[t]^2 + Abs[t]^4], 1/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4]}][
    t]/Norm[Derivative[
     1][{t^2/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4], (1. t)/Sqrt[
      1 + 1. Abs[t]^2 + Abs[t]^4], 1/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4]}][
     t]]
  .
  Norm[Derivative[
     1][{t^2/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4], (1. t)/Sqrt[
      1 + 1. Abs[t]^2 + Abs[t]^4], 1/Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4]}][
     t]]/(Sqrt[1 + 1. Abs[t]^2 + Abs[t]^4])

I'm not sure how to make it look nice on the forums here sorry.  But it's not evaluating the Norm or derivative at some places.  It also has a lot of Abs which I don't know if they are totally necessary.  How can I get this to to work?
The second one is a problem with taking derivatives.  

In[217]:= f[x_, y_, z_] := ((x^2)*(y^3)) + (z^4)
fx = Derivative[1, 0, 0][f][x, y, z]
fy = Derivative[0, 1, 0][f][x, y, z]
fz = Derivative[0, 0, 1][f][x, y, z]
x1[p_] := p + (3*(p^2))
dxdp = Derivative[1][x1][p]
y1[p_] := p*(E^p)
dydp = Derivative[1][x1][p]
z1[p_] := p*Sin[p]
dzdp = Derivative[1][x1][p]
Print["dF/dP:"]
Print[(fxdxdp) + (fydydp) + (fz + dzdp)]

The result:

Out[218]= 32 Sin[t] Sin[2 t]^3
Out[219]= 48 Sin[t]^2 Sin[2 t]^2
Out[220]= 32 Sin[3 t]^3
Out[222]= 1 + 6 p
Out[224]= 1 + 6 p
Out[226]= 1 + 6 p

During evaluation of In[217]:= dF/dP:
During evaluation of In[217]:= 1+6 p+48 (1+6 p) Sin[t]^2 Sin[2 t]^2+32 (1+6 p) Sin[t] Sin[2 t]^3+32 Sin[3 t]^3
Why am I getting Sins and t variables for a derivative of a xy function with no cos or sins?  This has happened on multiple problems for me.
Any and all help is welcome!
Thanks much!
 A: The following seems to work:
r[t_]:={t^3/3,t^2/2,t}
ta[t_]:=Simplify[r'[t]/Norm[r'[t]],Assumptions->Element[t,Reals]]
n[t_]:=Simplify[ta'[t]/Norm[ta'[t]],Assumptions->Element[t,Reals]]
c[t_]:=Simplify[Norm[ta'[t]]/Norm[r'[t]],Assumptions->Element[t,Reals]]
Then
ta[t] gives
$$
\left\{\frac{t^2}{\sqrt{t^4+t^2+1}},\frac{t}{\sqrt{t^4+t^2+1}},\frac{1}{\sqrt{t^4+t^2+1}}\right\}
$$
and n[t] gives
$$
\small\left\{\frac{t \left(t^2+2\right)}{\sqrt{\left(t^4+t^2+1\right) \left(t^4+4
   t^2+1\right)}},\frac{1-t^4}{\sqrt{t^8+5 t^6+6 t^4+5 t^2+1}},-\frac{2
   t^3+t}{\sqrt{\left(t^4+t^2+1\right) \left(t^4+4 t^2+1\right)}}\right\}
$$
and c[t] gives
$$
\sqrt{\frac{t^4+4 t^2+1}{\left(t^4+t^2+1\right)^3}}
$$

If your variables have had values assigned to them, and have not been Cleared, those values will be used. For example, if I have set
x=2Sin[t]
y=2Sin[2t]
z=2Sin[3t]
f[x_,y_,z_]:=((x^2)*(y^3))+(z^4)
then
Derivative[1,0,0][f][x,y,z] returns $32 \sin (t) \sin ^3(2 t)$
Derivative[0,1,0][f][x,y,z] returns $48 \sin ^2(t) \sin ^2(2 t)$
Derivative[0,0,1][f][x,y,z] returns $32 \sin ^3(3 t)$
If I clear the variables with Clear[x,y,z], 
Derivative[1,0,0][f][x,y,z] returns $2 x y^3$
Derivative[0,1,0][f][x,y,z] returns $3 x^2 y^2$
Derivative[0,0,1][f][x,y,z] returns $4 z^3$
