= Solution
Any nonsingular <holomorphic function> $f(\Phi_1,\ldots,\Phi_n)$ of <chiral superfields> is itself a <chiral superfield>. The <graded Leibniz rule> and the <chain rule> give
$$
\boxed{\bar D_{\dot\alpha}f(\Phi)=\sum_i\frac{\partial f}{\partial\Phi_i}\bar D_{\dot\alpha}\Phi_i=0.}
$$
Thus sums, products, convergent power series and inverses on patches where the denominator is nonzero preserve chirality. An ordinary function involving $\Phi^\dagger$ is generally not chiral, because $\bar D\Phi^\dagger$ need not vanish. This is why a <superpotential> is holomorphic. Spacetime derivatives also commute with $\bar D$, so derivatives of <chiral superfields> remain chiral; chirality by itself does not impose <renormalizability>.
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