## Calculus: Early Transcendentals 8th Edition

The expression is $$m_{tan}=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}.$$
By definition, the slope of the tangent line of the function $f$ at the point $P(a,f(a))$ is given by $$m_{tan}=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}.$$