anonymous
  • anonymous
Find the derivative of f(x) = 8 divided by x at x = -1. 4 0 8 -8 @ganeshie8 @hero @dan815 @perl @pooja195 @solomonzelman @mathstudent55 @zepdrix @usukidoll @
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
zepdrix
  • zepdrix
Remember your exponent rule? :)\[\Large\rm \frac{1}{x}=x^{-1}\]
anonymous
  • anonymous
no i dont; i dont know anything
zepdrix
  • zepdrix
\[\Large\rm f(x)=\frac{8}{x}\]Applying this exponent rule,\[\Large\rm f(x)=8x^{-1}\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

zepdrix
  • zepdrix
Then simply apply your power rule to take derivative! :) The -1 comes down to multiply, then subtract 1 from the exponent. ya?
anonymous
  • anonymous
would it be 8? @zepdrix
zepdrix
  • zepdrix
Hmm no :o
zepdrix
  • zepdrix
how'd you get 8?
anonymous
  • anonymous
wait never mind, why would i subtract?
zepdrix
  • zepdrix
\[\Large\rm f(x)=x^n\]Power rule tells us how to deal with polynomials,\[\Large\rm f'(x)=nx^{n-1}\]
zepdrix
  • zepdrix
Example:\[\Large\rm g(x)=4x^{3}\qquad\to\qquad g'(x)=4\cdot3x^{3-1}\]\[\Large\rm g'(x)=12x^{2}\]
zepdrix
  • zepdrix
you don't know anything? +_+ lol that's not good
anonymous
  • anonymous
i dont please help? @zepdrix can u take me step by step with my example
zepdrix
  • zepdrix
Nooo I don't wanna give you the answer :D I think you can do it. Let's work on a problem that's very similar. Given that \(\large\rm f(x)=\frac{4}{x^{2}}\) find f'(x) at x=2. We'll first write f(x) differently using our exponent rule,\[\large\rm f(x)=4x^{-2}\]Then we'll apply our power rule to take our derivative: The -2 comes down in front, and then we subtract 1 from the exponent:\[\large\rm f'(x)=4\cdot(-2)x^{-2-1}\]\[\large\rm f'(x)=-8x^{-3}\]Let's apply our exponent rule in reverse, putting the x back into the bottom,\[\large\rm f'(x)=\frac{-8}{x^3}\]Evaluating this function at x=2 gives us:\[\large\rm f'(2)=\frac{-8}{2^3}\]\[\large\rm f'(2)=-1\]
zepdrix
  • zepdrix
yayyy :) there are some stepssss
zepdrix
  • zepdrix
When you apply your power rule, be careful when dealing with negative exponents! If we have a -1 exponent, subtracting 1 from that will not give us 0, it will give us -2
anonymous
  • anonymous
im not asking for the answer I'm just trying to go step by step with my example with you
anonymous
  • anonymous
@zepdrix
anonymous
  • anonymous
so next would be f(x)=8x
anonymous
  • anonymous
@zepdrix
zepdrix
  • zepdrix
no, we have 8x^(-1) :O it gains a power of -1 when it comes up
zepdrix
  • zepdrix
Then apply your power rule, the -1 comes down in front as a multiplier, and the power decreases to -2.\[\large\rm f'(x)=8(-1)x^{-2}\]Simplify before plugging in your value,\[\large\rm f'(x)=\frac{-8}{x^2}\]
zepdrix
  • zepdrix
Then plug in your -1 :)
anonymous
  • anonymous
so then its f(x)=-8/-1^2
anonymous
  • anonymous
what do i do next? @zepdrix
zepdrix
  • zepdrix
\[\large\rm f'(-1)=\frac{-8}{(-1)^2}\]ya, then simplify.
anonymous
  • anonymous
them it will be f(x)=-8/1 right? @zepdrix
anonymous
  • anonymous
so the answer would be 8? @zepdrix
zepdrix
  • zepdrix
-8/1 does not equal 8
anonymous
  • anonymous
so is the answer -8?
anonymous
  • anonymous
@zepdrix
anonymous
  • anonymous
but would f(-1)=-8/-1^2=8? @zepdrix
zepdrix
  • zepdrix
yes :)
zepdrix
  • zepdrix
-8
zepdrix
  • zepdrix
when you square -1, you get 1.
anonymous
  • anonymous
can you help me with another? @zepdrix
anonymous
  • anonymous
Find the derivative of f(x) = -12x2 + 9x at x = 6. -112.5 -135 -90 -108 @zepdrix

Looking for something else?

Not the answer you are looking for? Search for more explanations.