simple differentiation

I'm supposed to differentiate [(sqrt(x))+1]^2/x
I thought this would be fairly straightforward even though I haven't learnt how to differentiate multiplications and divisions of functions.
So I developed [(sqrt(x))+1]^2 to end up with x+2(sqrt(x))+1, which gives me the three terms x/x + 2(sqrt(x))/x + 1/x, which differentiating separately gives me the final result:
-1/x(sqrt(x)) - 1/(x^2)
But this is incorrect apparently, where did I go wrong?

You did not go wrong anywhere. The correct answer is

For further information you can refer to this link:

d/dx (1+sqrt(x))^2/x - Wolfram|Alpha

Quote:

---

Originally Posted by furor celtica

I'm supposed to differentiate [(sqrt(x))+1]^2/x
I thought this would be fairly straightforward even though I haven't learnt how to differentiate multiplications and divisions of functions.
So I developed [(sqrt(x))+1]^2 to end up with x+2(sqrt(x))+1, which gives me the three terms x/x + 2(sqrt(x))/x + 1/x, which differentiating separately gives me the final result:
-1/x(sqrt(x)) - 1/(x^2)
But this is incorrect apparently, where did I go wrong?

---

Try rearranging it into the format expected:



CB

the answer given is
1 - 1/(x(sqrt(x))) - 2/(x^3)
Is this just another form for the same result, or a legit mistake in the textbook?

Quote:

---

Originally Posted by furor celtica

the answer given is
1 - 1/(x(sqrt(x))) - 2/(x^3)
Is this just another form for the same result, or a legit mistake in the textbook?

---

That would be a mistake in the textbook.
That expression is not the derivative of [(sqrt(x))+1]^2/x.