f '(0)= lim(x-& gt； 0)[f(x)-f(0)]/(x-0)

= lim(x->； 0)f(x)/x

= lim(x->； 0)(x- 1)(x+2)(x-3)……(x+ 100)

=(0- 1)(0+2)(0-3)…(0+ 100)

=(- 1)^50 100!

= 100!

Introduction to derivatives:

Derivative, also called derivative function value. Also known as WeChat quotient, it is an important basic concept in calculus. When the independent variable x of the function y=f(x) generates an increment δ x at the point x0, if there is a limit a in the ratio of the increment δ y of the function output value to the increment δ x of the independent variable when δ x tends to 0, then A is the derivative at x0, which is denoted as f'(x0) or df(x0)/dx.

Derivative is the local property of function. The derivative of a function at a certain point describes the rate of change of the function near that point. If the independent variables and values of the function are real numbers, then the derivative of the function at a certain point is the tangent slope of the curve represented by the function at that point. The essence of derivative is the local linear approximation of function through the concept of limit. For example, in kinematics, the derivative of the displacement of an object with respect to time is the instantaneous velocity of the object.