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

Re: simple differentiation

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:

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

CB

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?

Re: simple differentiation

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.