Find the derivative of the function

y=3+8x-6(squareroot x)/x

First simplify 6sqrt(x)/x to 6x^(.5)*x^(-1) = 6x^(-1/2)

y = 3 + 8x - 6x^(-1/2)

dy/dx = 8 + 3x^(-3/2)

Jen

Best way to deal with root derivatives is to change it to whatever to the power of 1/2. So it will be y=3+8x-6x^1/2 over x. Then use the quotient rule to solve
y'= (8-3x^-1/2)(x) - (3+8x-6x^1/2) all over x^2
y'= (8x - 3x^1/2) - 3 - 8x + 6x^1/2 all over x^2
y'= 3x^1/2 - 3 over x^2
y'= 3(root x - 1)/x^2
there you go it's solved :)