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I am using pdflatex in Texmaker (implements TeXLive). Using the default font, the numerator text of the following fractions are aligned to a common baseline:

$$fracpartial xpartial t fracpartial ypartial t fracpartial z_jpartial t$$

However, using the newpxmath package results in the numerators becoming misaligned:

documentclassarticle
usepackagenewpxmath
begindocument
$$fracpartial xpartial t fracpartial ypartial t fracpartial z_jpartial t$$
enddocument

I would like to use New PX for math, but align the numerators as in the default font. I could use vphantom... to force the numerators to have the same height, but is there a more elegant way to do this?

The design of Palatino contains long descenders. When a math font is based Palatino, the various math font dimensions should be chosen to avoid unevenness, as much as possible.

There are many font dimensions governing the positions of numerator and denominator in a fraction. We can change two of them in newpxmath which are the most relevant.

documentclassarticle
usepackagenewpxmath

% Code modified from lmsnpxsy.fd
makeatletter
expandafterifxcsname npxmath@scaledendcsnamerelax
 letnpxmath@@scaled@empty%
else
 edefnpxmath@@scaleds*[csname npxmath@scaledendcsname]%
fi
DeclareFontFamilyLMSnpxsyprovidecommand setSYdimenssetSYdimensskewchar font =120
DeclareFontShapeLMSnpxsymn%
 <-> npxmath@@scaled zplsy
%
 fontdimen 8font=0.8fontdimen6font % was 0.677 of a quad
 fontdimen11font=0.8fontdimen6font % was 0.686 of a quad

makeatother

usepackagemathtools% for clap
newcommand*drawbaseline%
 claprule80pt0.4pt%


begindocument
[
begingathered
x,ydrawbaseline,z\
fracpartial xpartial t fracpartial ydrawbaselinepartial t fracpartial z_jpartial t fracpartial z_j_jpartial t\
fracpartial xpartial t fracpartial ypartial t fracpartial z_jpartial t fracpartial z_j_jpartial t\
endgathered
]
enddocument

Modifying font dimensions gives the most consistent look for all your fractions, but this requires your own aesthetic judgement.

Here, I changed the numerator raising dimension from 0.677 to 0.8 to give more room for long descender. I also changed the denominator dropping dimension from 0.686 to 0.8 for more even spacing both above and below the fraction bar.