Derivation formula of compound function: ① Let u=g(x), and derive f(u) as follows: f'(x)=f'(u)*g'(x), let u=g(x), a=p(u), and derive f'(x).

Let the domain of function y=f(u) be 4 102Du, that of function u=g(x) be Dx, and that of function u = g (x) be Mx. If Mx∩Du≦? Then, if any X in Mx∩Du passes through U, and there is a unique definite Y value corresponding to it, then a functional relationship between the variables X and Y obtained through the variable U is recorded as: y=f[g(x)], where X is called independent variable, U is intermediate variable, and Y is dependent variable (i.e. function) 1653.

Extended data

You can judge whether this function is a composite function by observing the form of independent variables. For example, f(x)=sin(x) and the independent variable is x, which is a simple function.

Another example is f(x)=sin? (x), although the independent variable is still x, the original function can also be regarded as f(u)=u? , the independent variable is u=sin(x), in this case, sin? (x) is a composite function.

Let the domain of function Y=f(u) be d, and the domain of function u=φ(x) be z. If D∩Z, then Y forms a function of x through u, which is called a compound function of x, and is denoted as Y=f[φ(x)]. X is an independent variable, y is a dependent variable and u is called an intermediate variable.