Differentiation of fractions.

Though tbh with the one given I would split the numerator and then you have 2 easy things to differentiate

Hi guys, im a little bit stuck.

how would you differentiate

2x+3
-------
x

I had 2-3x^-2

Also, would it be ok if you do it step by step so i can see where i went wrong

Ok. Would it ok if you expand on that, maybe provide a visual? Like how you would it.

$\frac{2x + 3}{x} = 2 + \frac{3}{x}$ which is basically $2 + 3x^{-1}$ using laws of indices.

Can you differentiate this function now?

I know the answer is -3x^-2, but i just don't understand where the 2 has gone.
This might be really easy to you, but i've just started this topic, today. So, please just bear with me if i don't understand it.

If you differentiate a constant it disappears

oh, so the 2 is like c in the formula ax^2+bx+c? and then becomes Dy/Dx = 2ax + b, but the c is missed out since it's a constant, and therefore is 0, well, that's what i have in my book anyway.

I know the answer is -3x^-2, but i just don't understand where the 2 has gone.
This might be really easy to you, but i've just started this topic, today. So, please just bear with me if i don't understand it.

Yes

You can think of 2 as being the same as 2x^0.
x^0 is always 1, no matter what x is, so that is why those two things above are the same.
If you try differentiating 2x^0, then you get 0, since you have to multiply the whole expression by 0 as part of differentiation. That's why a constant will always disappear when you differentiate it.

Thanks for the explanation, I understand it a lot more thanks to you rather than this book. I really need to buy a new maths a level book. What book would you suggest and where could i buy it from? Cos the one i have now is Edexcel Maths A level 2004 specification, and it only has 1 example for questions like this, and it explains it in a really weird way.