Having trouble with simplifying things

[smulc]

This isn't about any specific problem, I'm just hoping for a bit of advice. I've been out of education for a long time and am now doing an OU degree. I've passed the first level with high marks but have been struggling in some of the maths.

Basically, I've been doing calculus and the bit I'm struggling with is the simplifications. It seems like because I've had to start learning from scratch again I've had to move over things so quickly that some of the basics haven't sunk in.

For example, differentiating f(x) = √x / ln(4x)

I had no problem coming up with this

(ln(4x))(1/2√x) - (√x)(1/x)
(ln4x)²

But I didn't even know where to start with simplifying it. I have the answer now, and even looking at the answer I still can't do it myself. Can anyone recommend any material I could work through to help with things like this? I've looked at Khan academy but this seems to be too much of a general thing to be covered.

Thanks.

 

[STEMucator]

This isn't about any specific problem, I'm just hoping for a bit of advice. I've been out of education for a long time and am now doing an OU degree. I've passed the first level with high marks but have been struggling in some of the maths.

Basically, I've been doing calculus and the bit I'm struggling with is the simplifications. It seems like because I've had to start learning from scratch again I've had to move over things so quickly that some of the basics haven't sunk in.

For example, differentiating f(x) = √x / ln(4x)

I had no problem coming up with this

(ln(4x))(1/2√x) - (√x)(1/x)
(ln4x)²

But I didn't even know where to start with simplifying it. I have the answer now, and even looking at the answer I still can't do it myself. Can anyone recommend any material I could work through to help with things like this? I've looked at Khan academy but this seems to be too much of a general thing to be covered.

Thanks.

I'm assuming your function is to be read : $\frac{\sqrt{x}}{ln(4x)}$.

Let me give you some advice which may potentially make your life easier. Do NOT use the quotient rule. It's messy and hard to simplify things.

You can re-write something like $\frac{1}{x}$ as $x^{-1}$ or $\frac{1}{x^3}$ as $x^{-3}$. In general $\frac{1}{x^n}$ can be written $x^{-n}$.

You can also re-write roots like so $\sqrt[n]{x} = x^{ \frac{1}{n} }$.

Using these ideas for your function you can re-write it as :

$f(x) = (x^{1/2})(ln(4x))^{-1}$.

Now you can differentiate it much more easily using the power, product and chain rules.

 

[smulc]

Thanks, that does make it easier to deal with. I'm still having issues though, as the problem is I can't simply them. I know this is meant to be a basic step just to clean it up, but I just don't seem to be able to do it. Using your method of avoiding the quotient rule I came up with this (I wasn't sure how you typed the equation like that on here so I had to post a picture)

http://imageshack.us/photo/my-images/27/1uj1.jpg/

I'm struggling to arrange things like this to their simplest form. I'm hoping to find somewhere that I can get more practice in doing it, as I know it shouldn't be a problem and is meant to be straight forward.

 

[tiny-tim]

hi smulc!

(ln(4x))(1/2√x) - (√x)(1/x)
(ln4x)²

can't you see a way of simplifying (√x)(1/x) ?

 

[smulc]

hi smulc!


can't you see a way of simplifying (√x)(1/x) ?

I know that part would just be 1 / √x but I can't do much more than that

 

[tiny-tim]

I know that part would just be 1 / √x but I can't do much more than that

yes you can …

you can subtract it from the 1/(2√x) that comes just before it! ​