# Thread: Finding derivative example

1. ## Finding derivative example

Hi,

I hope someone can help. I'm trying to find the derivative at x = 4 for the following equation:

For some reason, I get the wrong solution when I don't factor out the expression before finding the derivative:

The actual solution for f^1(4) is apparently 12:

Help would be very much appreciated!

2. ## Re: Finding derivative example

product rule ...

$f'(x) = (1+2x^{0.5})(-1 + 1.5x^{0.5}) + (-x+x^{1.5})(x^{-0.5})$

$f'(4) = (1+4)(-1+3) + (-4+8)\left(\dfrac{1}{2}\right) = 10 + 2 = 12$

3. ## Re: Finding derivative example

In other words, (fg)' is not equal to f'g'. It is, as skeeter said, f'g+ fg'.

4. ## Re: Finding derivative example

okay good to know. I wasn't aware of the product rule until now... so thanks!