Question

Differentiate (x^2+4x+3)/sqrtx

Answer 1

it might be helpful to write \( \sqrt{x} = x^{\frac{1}{2}} \)
now you have two choices:
1) use the quotient rule d(u/v) = (u dv - v du)/v^2
or
2) write the x^½ "up top" as x^-½
and use the product rule d(uv) = u dv + v du

Answer 2

You can also avoid using quotient/product and reduce this to a power rule application:
\[\frac{x^2+4x+3}{x^{1/2}}=x^{3/2}+4x^{1/2}+3x^{-1/2}\]