Let $f$ be a transcendental meromorphic function on $\mathbb{ C}$, and $P(z), Q(z)$ be two polynomials with $\deg P(z)>\deg Q(z)$. In this paper, we prove that: if $f(z)=0\Rightarrow f^{\prime}(z)=a$(a nonzero constant), except possibly finitely many, then $f^{\prime}(z)-P(z)/Q(z)$ has infinitely many zeros. Our result extends or improves some previous related results due to Bergweiler–Pang, Pang–Nevo–Zalcman, Wang–Fang, and the author, et. al.