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I am suppose to differentiate $(x^2 +4x +3)/ \sqrt{x}$ I know that a square root is equal to $x^{1/2}$ but I still am not able to properly differentiate this problem. I ended up with $(2x+4)/ (1/2)x^{1/2})$ which I know is wrong.

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    That makes sense, thank you.2011-09-17

2 Answers 2

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Dividing through, your expression equals $ x^{3/2}+4x^{1/2}+3x^{-1/2}. $ Now you can use the power rule.

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You can also exercise your quotient rule: \left( \dfrac{f}{g}\right)^'=\dfrac{f'g-gf'}{g^2}.