# Re: Directional derivative in content MathML?

```I don't know if this was what you had in mind, but
given u=(x,y,z) with x,y and z all functions of s,
I would write df(x,y,z)/du  *du/ds  as something like

<apply>
<plus/>
<apply>
<times/>
<apply><partialdiff/><bvar><ci>x</ci></bvar>
<apply><ci>f</ci><ci>x</ci><ci>y</ci><ci>z</ci></apply>
</apply>
<apply><partialdiff/><bvar><ci>s</ci></bvar>
<apply><ci>x</ci><ci>s</ci></apply>
</apply>
</apply>
<apply>
<times/>
<apply><partialdiff/><bvar><ci>y</ci></bvar>
<apply><ci>f</ci><ci>x</ci><ci>y</ci><ci>z</ci></apply>
</apply>
<apply><partialdiff/><bvar><ci>s</ci></bvar>
<apply><ci>y</ci><ci>s</ci></apply>
</apply>
</apply>
<apply>
<times/>
<apply><partialdiff/><bvar><ci>z</ci></bvar>
<apply><ci>f</ci><ci>x</ci><ci>y</ci><ci>z</ci></apply>
</apply>
<apply><partialdiff/><bvar><ci>s</ci></bvar>
<apply><ci>z</ci><ci>s</ci></apply>
</apply>
</apply>
</apply>

I would write the gradient of f evaluated at (a,b,c) as

<apply>
<vector><ci>a</ci><ci>b</ci><ci>c</ci></vector>
</apply>

and if u is a unit vector I would write the directional derivative of f
in the direction uu=(u,v,w)  (a unit vector) at (a,b,c) as:

<apply>
<apply>
<times definitionURL="dotproduct"/>