Derive the following with respect to x1: y=(x1*x2)/(x1+x2).
y is a function of x1 and x2. We are asked to derive y with respect to x1, meaning that x2 remains constant.
Note that y' is the derivative of y.
Both the numerator and denominator of the fraction contain x1. Therefore, we will need to follow the quotient rule of differentiation.
dy/dx1=[ (x1*x2)' *(x1+x2) - (x1x2)(x1+x2)' ] / [(x1+x2)2] ,
dy/dx1=[x2*(x1+x2)-(x1*x2*1)]/ [(x1+x2)2],
Therefore: dy/dx1=x2/(x1+x2) - x1*x2/(x1+x2)2
