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anonymous

  • one year ago

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 @

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  1. zepdrix
    • one year ago
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    Remember your exponent rule? :)\[\Large\rm \frac{1}{x}=x^{-1}\]

  2. anonymous
    • one year ago
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    no i dont; i dont know anything

  3. zepdrix
    • one year ago
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    \[\Large\rm f(x)=\frac{8}{x}\]Applying this exponent rule,\[\Large\rm f(x)=8x^{-1}\]

  4. zepdrix
    • one year ago
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    Then simply apply your power rule to take derivative! :) The -1 comes down to multiply, then subtract 1 from the exponent. ya?

  5. anonymous
    • one year ago
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    would it be 8? @zepdrix

  6. zepdrix
    • one year ago
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    Hmm no :o

  7. zepdrix
    • one year ago
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    how'd you get 8?

  8. anonymous
    • one year ago
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    wait never mind, why would i subtract?

  9. zepdrix
    • one year ago
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    \[\Large\rm f(x)=x^n\]Power rule tells us how to deal with polynomials,\[\Large\rm f'(x)=nx^{n-1}\]

  10. zepdrix
    • one year ago
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    Example:\[\Large\rm g(x)=4x^{3}\qquad\to\qquad g'(x)=4\cdot3x^{3-1}\]\[\Large\rm g'(x)=12x^{2}\]

  11. zepdrix
    • one year ago
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    you don't know anything? +_+ lol that's not good

  12. anonymous
    • one year ago
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    i dont please help? @zepdrix can u take me step by step with my example

  13. zepdrix
    • one year ago
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    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:\[\large\rm f'(2)=\frac{-8}{2^3}\]\[\large\rm f'(2)=-1\]

  14. zepdrix
    • one year ago
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    yayyy :) there are some stepssss

  15. zepdrix
    • one year ago
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    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

  16. anonymous
    • one year ago
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    im not asking for the answer I'm just trying to go step by step with my example with you

  17. anonymous
    • one year ago
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    @zepdrix

  18. anonymous
    • one year ago
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    so next would be f(x)=8x

  19. anonymous
    • one year ago
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    @zepdrix

  20. zepdrix
    • one year ago
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    no, we have 8x^(-1) :O it gains a power of -1 when it comes up

  21. zepdrix
    • one year ago
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    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,\[\large\rm f'(x)=\frac{-8}{x^2}\]

  22. zepdrix
    • one year ago
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    Then plug in your -1 :)

  23. anonymous
    • one year ago
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    so then its f(x)=-8/-1^2

  24. anonymous
    • one year ago
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    what do i do next? @zepdrix

  25. zepdrix
    • one year ago
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    \[\large\rm f'(-1)=\frac{-8}{(-1)^2}\]ya, then simplify.

  26. anonymous
    • one year ago
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    them it will be f(x)=-8/1 right? @zepdrix

  27. anonymous
    • one year ago
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    so the answer would be 8? @zepdrix

  28. zepdrix
    • one year ago
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    -8/1 does not equal 8

  29. anonymous
    • one year ago
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    so is the answer -8?

  30. anonymous
    • one year ago
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    @zepdrix

  31. anonymous
    • one year ago
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    but would f(-1)=-8/-1^2=8? @zepdrix

  32. zepdrix
    • one year ago
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    yes :)

  33. zepdrix
    • one year ago
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    -8

  34. zepdrix
    • one year ago
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    when you square -1, you get 1.

  35. anonymous
    • one year ago
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    can you help me with another? @zepdrix

  36. anonymous
    • one year ago
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    Find the derivative of f(x) = -12x2 + 9x at x = 6. -112.5 -135 -90 -108 @zepdrix

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