text: the derivative of (sq.rt.(x))+1/(sq.rt.(x))-1? can you please show the entire process? sq. rt (x)= x^(1/2); 1/(sq.rt.(x)= x^(-1/2); so your expression is x^(1/2) + x^(-1/2) - 1. the first derivative of the sum of the three parts is the sum of the first derivatives of each part. d[x^(1/2)]/dx = 1/2*[x^(-1/2)]; d[x^(-1/2)]/dx = -1/2*[x^(-3/2)]; d(1)/dx = 0. add the parts and you get: 1/2*[x^(-1/2)] - 1/2*[x^(-3/2)] + 0. if you want to collect terms you can factor out 1/2*[x^(-1/2)], and then you would have 1/2*[x^(-1/2)]*[1- (1/x)]. there are many ways to factor the derived expression, and all would be correct if you stay within the rules of mathematics. as my ancient professor would say, "it's all intuitively obvious, isn't it?"