The derivative is defined as: f′(x)=limΔx→0f(x+Δx)−f(x)Δx Graphically, the derivative of a function represents the slope of the fu...The derivative is defined as: f′(x)=limΔx→0f(x+Δx)−f(x)Δx Graphically, the derivative of a function represents the slope of the function, and it is positive if the function is increasing, negative if the function is decreasing and zero if the function is flat.