The concept of differentiation is produced in solving the contradiction between straight and curved. In tiny parts, straight lines can be used instead of curves to approximate, and its direct application is the linearization of functions. Differential has a double meaning: it represents a tiny quantity, so the numerical calculation result of a linear function can be regarded as the numerical approximation of the original function, which is the basic idea of approximate calculation by differential method.
If the change of function y=f at x point △y=f-f can be expressed as △y=A△x+α,
Where a has nothing to do with △x, and α is the high-order infinitesimal of △x, then A△x is called the differential of the function y=f at X, and it is denoted as dy, that is, Dy = A △ X, and the function y=f is called differentiable at X. ..
The derivative f of the function is equal to the quotient of the differential dy of the function and the differential dx of the independent variable. Therefore, it is also called WeChat business. Dy/dx is often treated as a complete symbol, so by using the relationship between differential and derivative, dy/dx can be treated as a fraction, which brings a lot of convenience to calculation.