# Can't solve this simple derivative

1. Nov 3, 2012

### Hemolymph

Can someone please show me how to get the derivative of (-x^2/18). I know the answer is x/9 but I use the quotient rule and keep getting (x^2-36x)/18^2

Thanks b

Last edited: Nov 3, 2012
2. Nov 3, 2012

### Xishem

Instead of using the quotient rule, try writing the function as:

$\frac{1}{18}x^2$

Now it is just a power rule derivative. Does that help?

Not that the quotient rule doesn't work, though. From your answer, it looks like you're doing it incorrectly. Remember that the quotient rule is:
$$\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}$$

Last edited: Nov 3, 2012
3. Nov 3, 2012

### Hemolymph

So I did (1/18)(x^2)

To get 2x(1)+(1/18)(x^2)

2x+(x^2/18)

(36x+x^2)/18

what can i do after that step?

4. Nov 3, 2012

### Xishem

You're using the power rule incorrectly also. The power rule is:
$$\frac{d}{dx}cx^n=ncx^{n-1}$$Edit: Ah, it looks you are trying to do the product rule. Remember that if you have any constant times x or x divided by a constant, you can use the power rule instead of the product or quotient rules.

Remember that the derivative of a constant term is 0, not 1!

Still, once again, the power rule does work in this case. It is:
$$\frac{d}{dx}f(x)g(x)=f'(x)g(x)+f(x)g'(x)$$

Last edited: Nov 3, 2012
5. Nov 3, 2012

### Hemolymph

whoops it should have been -x^2+36x/18^2 for the quotient rule

6. Nov 3, 2012

### Hemolymph

Yea thanks I just had a small mental break down was making stupid mistakes
I get (18x^2+2x)/18

7. Nov 3, 2012

### Xishem

Let's try this first:

What is $\frac{d}{dx}x^2$ ?

8. Nov 3, 2012

### Hemolymph

it would be 2x

9. Nov 3, 2012

### Ray Vickson

What is
$$\frac{d}{dx} \left(\frac{1}{18}\right) \, ?$$

RGV

10. Nov 3, 2012

### Hemolymph

a constant so one

11. Nov 3, 2012

### Xishem

The derivative of a constant is 0.

12. Nov 3, 2012

### Hemolymph

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13. Nov 3, 2012

### Hemolymph

WOW im such a fool...

14. Nov 3, 2012

### Hemolymph

alright I got it now......(2x/18)=x/9

Thanks everyone for your help much appreciated

15. Nov 3, 2012

### Staff: Mentor

A couple more points that weren't brought up in this thread:

1. You should never use the quotient rule if the denominator is a constant. It's not wrong to use the quotient rule, but it's more complicated, which makes it more likely that you will make a mistake.

For example, if f(x) = x2/4, write this as (1/4)x2 and use the constant multiple rule, which says that d/dx(k*f(x)) = k*d/dx(f(x)).
Using this rule we get f'(x) = (1/4) * d/dx(x2) = (1/4) * 2x = x/2

2. You should never use the product rule if one factor is a constant. Instead, use the constant multiple rule. It would not be incorrect to use the product rule, but as before, it's more complicated, so you are more likely to make a mistake.

For example, if g(x) = 10 * tan(x), then g'(x) = 10 * d/dx(tan(x)) = 10 * sec2(x).

16. Nov 5, 2012

### Hemolymph

Thanks that definitely helped me