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anonymous

  • one year ago

derrivate h(t)=3e^-6t*t^7*(t+6)^3 I thought it would be -18te^-6t*7t^6*3(t+6)^2+t PLEASE HELP

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  1. sweetburger
    • one year ago
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    you should put parenthesis around stuff because im not sure if this all exponents to exponents

  2. zepdrix
    • one year ago
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    \[\Large\rm h(t)=3e^{-6t} \cdot t^{7} \cdot (t+6)^3\]This?

  3. zepdrix
    • one year ago
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    You'll have to apply your product rule, it will look kinda complicated since you have three terms though:\[\Large\rm (uvw)'=u'vw+uv'w+uvw'\]

  4. zepdrix
    • one year ago
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    Or you can use logarithmic differentiation if that approach I mentioned sounds too rough

  5. anonymous
    • one year ago
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    \[h(t)=3e ^{-6t}*t ^{7}* (t+6)^{3}\] is the equation What I thought: \[-18te ^{-6t}*7t ^{6}*3(t+6)^{2}+t\]

  6. anonymous
    • one year ago
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    ok Ill use the product rule, give me just a moment, Ill try to solve it.

  7. zepdrix
    • one year ago
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    Setup would look something like that I suppose :) Differentiating the blue stuff.

  8. zepdrix
    • one year ago
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    ahh woops i made a boo boo ;c there we go \[\rm h'(t)=\color{royalblue}{(3e^{-6t})'} \cdot t^{7} \cdot (t+6)^3\quad+\quad 3e^{-6t} \cdot \color{royalblue}{(t^{7})'} \cdot (t+6)^3\]\[\rm \qquad+\quad 3e^{-6t} \cdot t^{7} \cdot \color{royalblue}{((t+6)^3)'}\]

  9. anonymous
    • one year ago
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    yup I did exactly that can I'll just write the blue on every hope u understand. The first blue would be -18e^-6t, second: 7t^6. last: 3(t+6)+t. I just putthem together with the black, but that answer doesnt match the one in my book, why they gotta always mess things up....I follow their rules and stuff they never follow their own.

  10. anonymous
    • one year ago
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    opps last one, (3(t+6)^2)+t

  11. zepdrix
    • one year ago
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    woops, last blue should give us this:\[\Large\rm \color{royalblue}{\frac{d}{dx}(t+6)^3}=3(t+6)^2\color{royalblue}{(t+6)'}=3(t+6)(1)\]ya?

  12. zepdrix
    • one year ago
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    Derivative of t+6 = 1+0

  13. anonymous
    • one year ago
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    Yes ofc, silly misstake.their answer tho is: \[-6te^{-6t}*(t+6)^{2}*(3t ^{2}+13t-21)\] HOW?!

  14. zepdrix
    • one year ago
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    We have to do some factoring :) Books tends to over simplify, sall good, we can get there.

  15. zepdrix
    • one year ago
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    So what does everything have? They each have the exponential, ya? How many t's do they all have? Well they all have at least 6 t's multiplying. t^6 And they all have a factor of 3, right? :d See where we're going with this?

  16. zepdrix
    • one year ago
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    |dw:1434882566785:dw|

  17. zepdrix
    • one year ago
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    We want to pull out the greatest common factor that each term shares.

  18. zepdrix
    • one year ago
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    |dw:1434882683506:dw|So we pull that out.