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Let $f$ be a transcendental meromorphic function in the complex plane$\mathbb{C}$, and $a$ be a nonzero complex number . We give quantitativeestimates for the characteristic function $T(r,f)$ in terms of$N(r,1/(f^l(f^{(k)})^n-a))$, for integers $k$, $l$, $n$ greater than 1. Weconclude that $f^l(f^{(k)})^n$ assumes every nonzero finite value infinitelyoften.

A note on the value distribution of $f^l(f^{(k)})^n$