Find the derivative of f(x) = negative 6 divided by x at x = 12.

Question

anonymous · Answer

$$f(x) = - \frac{ 6 }{ x }$$ this?

anonymous · Answer

yes

anonymous · Answer

Alright so any idea how to find the derivative? Hint: Power rule

anonymous · Answer

No I am new to this lesson

anonymous · Answer

Do you know of the power rule?

anonymous · Answer

No

anonymous · Answer

$$\frac{ d }{ dx } x^n \implies n x^{n-1}$$

anonymous · Answer

Power rule, as you can see you just bring the exponent down, and subtract by 1 in the exponents

anonymous · Answer

So for an example, if I say find the derivative of $$x^9$$ all you'd do is $$f'(x) = 9x^8$$

anonymous · Answer

so would it be
f(x)=2x^(-6/x-1)??

anonymous · Answer

Mhm, not sure what you did there, where did 2x come from?

anonymous · Answer

Sorry I meant 12 because it says at x=12

anonymous · Answer

Well what I suggest is, you find the derivative first then plug in 12 for x.

anonymous · Answer

Ohh ok so f(x)=x^-6x-1?

anonymous · Answer

No, that's not right. The calculus part is easy, the main thing here is knowing your exponent rules. What can we do with $$\frac{ 1 }{ x }$$

anonymous · Answer

If I asked you to do use the power rule, how would you do it, just with 1/x

anonymous · Answer

Think back to exponents

anonymous · Answer

Ok I would do f(x)x^(1/x-1)

anonymous · Answer

oh wait is it 1/x^(1/x-1)?

anonymous · Answer

No no, you're over thinking this, note that $$\frac{ 1 }{ x } \implies x^{-1}$$ right?

anonymous · Answer

yes

anonymous · Answer

So the derivative would just be, $$\large -x^{-2} \implies -\frac{ 1 }{ x^2 }$$

anonymous · Answer

Ohhh ok that makes sense

anonymous · Answer

Yup! Now what would be the derivative of $$f(x) = -\frac{ 6 }{ x }$$

anonymous · Answer

f(x)=-6x^-7

anonymous · Answer

-7?

anonymous · Answer

I think you need to review your exponent rules, which I made a very short tutorial for, you can find it here: http://openstudy.com/users/iambatman#/updates/54ff9b2ce4b064b5a94d524c

anonymous · Answer

Ok Im currently looking. I might take a while  but I'll message you back

anonymous · Answer

Np, take as much time as you like, I don't want to give you the answer because you will not learn that way, so when ever you're ready go ahead and post what you think it is :) Good luck.

anonymous · Answer

Ok I'm back so the derivative would be 6/x^2

anonymous · Answer

Good!

anonymous · Answer

Finally! what do I do with the x at 12 part?

anonymous · Answer

Now you have the derivative, you simply plug it in for x :)

anonymous · Answer

Oh! so the answer is 1/24!

anonymous · Answer

Yup :)!

anonymous · Answer

Yay! Thank you so much @iambatman  for helping me :)

anonymous · Answer

No problem, take care!