Is $\lim_{h\to0} \frac{f(x+h(x-y))-f(x)}{h} \geq f'(x)(x-y)$?

Is $\lim_{h\to0} \frac{f(x+h(x-y))-f(x)}{h} \geq f'(x)(x-y)$ for a differentiatable function $f$?

I came across this problem and in the accepted solution, the author follows that the above is true, but I don't understand why this should be the case, since obviously $\lim_{h\to0} \frac{f(x+h)-f(x)}{h} = f'(x)$.