# Derive a fraction

1. Jun 2, 2010

### ghostbuster25

Does anyone know how to derive a fraction?

I want to be able to differentiate f(x)=$$\frac{x(20-x)}{36}$$

Ill show you what ive done but think ive just simplified it.

f(x)=$$\frac{x(20-x)}{36}$$

f(x)=$$\frac{(20-x-x)}{36}$$

f(x)=$$\frac{(10-x)}{18}$$

Is this correct?...........although not sure what the rule ive followed is :(

2. Jun 2, 2010

### Dickfore

Actually, it's not a fraction, since the argument occurs only in the numerator. Therefore, it is simply a polynomial with coefficients
that are fractions.

3. Jun 2, 2010

### LCKurtz

Nope. It is equal to

$$\frac{20x -x^2}{36}$$

That last expression is the correct answer for the derivative, but only the Shadow knows why it all worked out to be the derivative, and why aren't you calling it f'(x)?

4. Jun 2, 2010

### ghostbuster25

Im not sure what i have done then. I understand what you mean and how to differntiate polynominals(not very well) but i think what is throwing me is no exponent like x^3=3x^2 as its deivative.
Is my solution correct?

5. Jun 2, 2010

### Dickfore

Actually, he used the product rule for $x^{2} = x \cdot x$.

6. Jun 2, 2010

### LCKurtz

Yeah, I see now what he did. And he didn't call it f'(x) when he took the derivative.

7. Jun 2, 2010

### ghostbuster25

I get it!!!

ok let me show you to mke sure

f(x)=$$\frac{x(20-x)}{36}$$

f(x)=$$\frac{(20x-x^2)}{36}$$

f(x)=$$\frac{(20x-2x)}{36}$$

f'(x)=$$\frac{1x}{2}$$

that correct? although not f(x)=$$\frac{(10-x)}{18}$$ as you said....??

8. Jun 2, 2010

### LCKurtz

That step isn't correct. If you are differentiating you should call it f'(x). And the derivative of 20x isn't 20x.

9. Jun 2, 2010

### ghostbuster25

ok so derivative of 20x is 20.....derivative of x^2 is 2x?
would that make it 20-2x/36......which is 20-2x/36 which is 1/-2x/18

that correct? sorry i know im going the long way about this i just really want to understand what im doing :)

10. Jun 2, 2010

### Char. Limit

If by "1/-2x/18" you meant $$\frac{10-2x}{18}$$, then yes.

11. Jun 2, 2010

### Dickfore

Also, please note that 'derive' is not the correct term. In English, to derive means deduce a formula by doing some algebraic manipulations. The process of finding the derivative is called differentiation.

12. Jun 2, 2010

### ghostbuster25

ha ha yes i did mean that. Thankyou for your help. Did LCKurtz make a mistake when he said 10-x/36 was correct?

13. Jun 2, 2010

### LCKurtz

No, I didn't. (20-2x)/36 = 2(10-x)/36 = (10-x)/18.

14. Jun 2, 2010

### Mu naught

Before you even differentiate, pull the 1/36 out as a constant, and distribute the X to get:

20X - X2

then differentiate that, and multiply by the constant again and simplify.

15. Jun 2, 2010

### ghostbuster25

ok thanks, sorry for ignorance but........why did you do that and not leave it as 2x?

16. Jun 2, 2010

### Mu naught

Because X(20-X) = 20X - X2