The derivative of piecewise function, piecewise derivative, at the breakpoint, if the derivatives on both sides are equal, piecewise derivatives can be connected.

For example, when x is not equal to 0, f (x) = x 2 * [cos1/x], and when x=0, f(x)=a,

f(x)=x^2,x<； 0，f(x)=0，x & gt=0;

When x is less than 0, f' (x) = 2x; When x is greater than 0, f' (x) = 0;

At 0, the left derivative = 2 * 0 = 0; Right derivative = 0;

Left = right; And f(x) is continuous.

So the derivative at 0 =0.