# Thread: simple differentiation

1. ## 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?

2. ## Re: simple differentiation

You did not go wrong anywhere. The correct answer is $\displaystyle -\frac{1}{x^2}-\frac{1}{x\sqrt{x}}$

For further information you can refer to this link:

d&#47;dx &#40;1&#43;sqrt&#40;x&#41;&#41;&#94;2&#47;x - Wolfram|Alpha

3. ## Re: simple differentiation

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:

$\displaystyle -\frac{1}{x\sqrt{x}}-\frac{1}{x^2}=-\frac{1}{x^{3/2}}-\frac{1}{x^2}=-\frac{1}{x^2}(\sqrt{x}+1)$

CB

4. ## Re: simple differentiation

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?

5. ## Re: simple differentiation

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.