Consider the function y = x (1/2), which has the inverse function x = y 2. [x^( 1/2)]'= 1/(y^2)'= 1/(2y)= 1/[2x^( 1/2)]=( 1/2)x^(- 1/2)。 When using the inverse function to derive, be careful not to write the inverse function x = y 2 as y = x 2 according to the habit.

The derivative of the inverse function is the reciprocal of the original function. Example: Find the derivative function of y=arcsinx, and the derivative of the inverse function is the reciprocal of the derivative of the original function. First of all, the inverse function of function y=arcsinx is x=siny, so: y' =1/sin' y =1/cosy, because x=siny, cosy=√ 1-x2, so y' =1.

derivative

If the function y=f(x) is differentiable at every point in the open interval, it is said that the function f(x) is differentiable in the interval. At this time, the function y=f(x) corresponds to a certain derivative value for every certain value of x in the interval, and forms a new function, which is called the derivative function of the original function y=f(x), and is abbreviated as y', f'(x), dy/dx or df(x)/dx.

Derivative is an important pillar of calculus. Newton and Leibniz contributed to this.

Reference to the above content: Baidu Encyclopedia-Derivation