= Second-order relative change of a monomial
{title2=$\Delta f/f=ph+qj+\tfrac12p(p-1)h^2+pqhj+\tfrac12q(q-1)j^2+O((|h|+|j|)^3)$}
For positive $a,b$, fixed real $p,q$, and $f(a,b)=a^pb^q$, change the inputs to $a(1+h),b(1+j)$ with $h,j$ small. The ratio of the new value to the old one is exactly $(1+h)^p(1+j)^q$. Applying the <binomial series> to each factor and multiplying proves the displayed <Taylor expansion>. Positive inputs and $1+h,1+j>0$ make arbitrary real exponents well defined. A percentage change of $k$ in $a$ means $h=k/100$, not $h=k$. The mixed term $pqhj$ is required even though there is no such term in either one-variable expansion separately.
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