Derivative of (2x^2 + 1)x^(1/2) using Product Rule | Homework Question

[dh743]

Homework Statement

Find the derivative of y= (2x² + 1) x^1/2

Homework Equations

Product Rule

The Attempt at a Solution

After differentiating, I eventually get stuck at:
\frac{4x^3/2+2x²+1}{2\sqrt{x}}

The given solution is \frac{10x²+1}{2\sqrt{x}}

 

[adriang]

the problem is in your algebra, on the left you have, after differentiating, (x^1/2)4x, now when putting it over a common denom, you get 2x^1/2[(x^1/2)4x] which becomes 2x times 4x... from here i think u can finish it correctly
edit: or the way you've done it, (4x^3/2) which is the left, you need to times it by the common denom, so 4x^3/2 times 2x^1/2