=(r+x)/ √(r^2-x^2)

s `=[(r+x)`×√(r^2-x^2)-(r+x)×[√(r^2-x^2)]`]/(r^2-x^2]

=[√(r^2-x^2)-(r+x)×[( 1/2)/√(r^2-x^2)]×(r^2-x^2)`]/(r^2-x^2)

=[√(r^2-x^2)-(r+x)×[( 1/2)/√(r^2-x^2)]×(-2x)`]/(r^2-x^2)

=[√(r^2-x^2)+(r+x)x/√(r^2-x^2)]`]/(r^2-x^2)

= 1/[√(r^2-x^2)+x(r+x)/√[(r^2-x^2)^3)

(1) The derivative of the fractional function: it is a fraction; the denominator is the square of the original denominator; The numerator is the derivative of the numerator of the original fraction-the numerator of the original fraction multiplied by the derivative of the denominator;

(2) Derivative of denominator: = [√ (R2-X2) ]` = [(R2-X2) (1/2) ]`

=( 1/2)×(r^2-x^2)^(- 1/2)×(r^2-x^2)`

This is the derivative of the compound function: to √ (r 2-x 2), first take the derivative of the whole variable (r 2-x 2).

Multiply by (r 2-x 2) and take the derivative of x: (r 2-x 2) ` =-2x.