Question

Differentiate the following function.
y = (5 x^2 + 7 x + 6)/sqrt(x)

Answer 1

use the quotient rule

h(x)=&#131(x)/g(x)

h&prime(x)=[&#131 &prime (x)*g(x) - g&prime (x)*&#131 (x)]/g(x)²

Answer 2

You could use the quotient rule, but why not try this approach

y = (5 x^2 + 7 x + 6)/sqrt(x)
= 5x^(3/2) + 7x^(1/2) + 6x^(-1/2)
now
dy/dx = (15/2)x^(1/2) + (7/2)x^(-1/2) - 3x^(-3/2)
= (1/2)x^(-3/2)[15x^2 + 7x - 6]
= (15x^2 + 7x - 6)/(2x√x)

check my algebra carefully.