3. Derivative notation We have seen that the limit definition of the f at a is written as f'(a) = lim flat h) - f(a) h-+0 h In general, f'(x) is a function itself, and it represents the first derivative of f(r). This "prime" notation comes from Joseph Louis Lagrange. Additionally, we also use Leibniz notation to describe derivatives (named for Gottfried Leibniz). In general, this notation looks like a fraction with the numerator specifying the original function, and the denominator specifies the variable of the function. Leibniz notation can written in several different ways to describe the first derivative of a function y = f(x): f'(x) = f(x) : "The derivative with respect to z of f(z)" (1) f'(x) = of : "The derivative of f(r) with respect to a" (2) ay f'(x) = ar : "The derivative of y with respect to r" (3) (a) Use all three versions of Leibniz notation to write, by hand, the derivative of the function = = w(0). Include your description in words next to each form. (b) To describe the derivative at a point using Leibniz notation, we write of ar zza : "The derivative of f evaluated at a Use this Leibniz notation to describe w(a), the first derivative of w at a