Thread: Simple differentiation problem using product rule

1. Simple differentiation problem using product rule

I'm doing a seemingly simple problem for h.w

The question is to differentiate (u − squareroot of u)(u+ squareroot of u)

After applying the product rule I get 2u-1-u^1/2 However when I input it the h.w says it's wrong. can someone please help me?

2. Re: Simple differentiation problem using product rule

I would first rewrite the function as follows:

$f(u)=(u-\sqrt{u})(u+\sqrt{u})=u^2-u$

Now, differentiation is a bit simpler.

3. Re: Simple differentiation problem using product rule

but doesn't that disregard the product rule? If i differentiate that I get 2u-1

4. Re: Simple differentiation problem using product rule

It allows you to dispense with the product rule, but you will get the same result either way. It's just simpler in this case to find the product first, then differentiate.

5. Re: Simple differentiation problem using product rule

Of course, MarkFL2 is correct. The derivative is the same no matter how you find it, so you may as well find it the easiest way. But if you really want to use the product rule, here it is:

$f'(u)=(u-\sqrt{u})(u+\sqrt{u})'+(u-\sqrt{u})'(u+\sqrt{u})$
$=(u-\sqrt{u})(1+\frac{1}{2\sqrt{u}})+(1-\frac{1}{2\sqrt{u}})(u+\sqrt{u})$
$=(u-\sqrt{u}+\frac{\sqrt{u}}{2}-\frac{1}{2})+(u+\sqrt{u}-\frac{\sqrt{u}}{2}-\frac{1}{2})$
$=2u-1$

- Hollywood