Easy, type
In[11]:= Positive[Derivative[1][h][x_]] ^:= True
and check
In[12]:= Positive[h'[p]]
Out[12]= True
In[13]:= NonNegative[h'[p]]
Out[13]= NonNegative[Derivative[1][h][p]]
In[15]:= Negative[h'[q]]
Out[15]= Negative[Derivative[1][h][q]]
In[16]:= Positive[k'[p]]
Out[16]= Positive[Derivative[1][k][p]]
In[19]:= Positive[h''[q]]
Out[19]= Positive[(h^\[Prime]\[Prime])[q]]
In[32]:= Positive[h'[q, p]]
Out[32]= Positive[Derivative[1][h][q, p]]
