How Do You Correctly Derive (-x^2/18)?

[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

 

[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:
$$\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}$$

 

[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?

 

[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:
$$\frac{d}{dx}f(x)g(x)=f'(x)g(x)+f(x)g'(x)$$

 

[Hemolymph]

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

 

[Hemolymph]

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

 

[Xishem]

Let's try this first:

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

 

[Hemolymph]

Let's try this first:

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

it would be 2x

 

[Ray Vickson]

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?

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

RGV

 

[Hemolymph]

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

RGV

a constant so one

 

[Xishem]

The derivative of a constant is 0.

 

[Hemolymph]

------

 

[Hemolymph]

The derivative of a constant is 0.

WOW I am such a fool...

 

[Hemolymph]

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

Thanks everyone for your help much appreciated

 

[Mark44]

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).

 

[Hemolymph]

Thanks that definitely helped me