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Thread: Calculate f'(x)

  1. October 21st 2010, 09:26 AM #1
    Lil
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    Calculate f'(x)

    f(x)=tg x \cdot e^{3x}
    f'(x)=(tg x \cdot e^{3x})'=...

    What rule I can use to solve this? I need examples like this tasks or something
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  2. October 21st 2010, 09:27 AM #2
    Ackbeet
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    Are t and g considered constant?
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  3. October 21st 2010, 09:28 AM #3
    Lil
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    It's tg(x)
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  4. October 21st 2010, 09:31 AM #4
    Ackbeet
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    Is that the tangent function, then?
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  5. October 21st 2010, 09:33 AM #5
    Lil
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    Quote Originally Posted by Ackbeet View Post
    Is that the tangent function, then?
    Yes.
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  6. October 21st 2010, 09:34 AM #6
    Ackbeet
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    Ah. Standard notation is

    (\tan(x)e^{3x})'.

    What rule do you think would be appropriate here?
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  7. October 21st 2010, 09:36 AM #7
    Also sprach Zarathustra
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    Yes, mr. Ackbeet it is tan(x)....

    Appalling the chain rule...

    f'(x)=(tag x \cdot e^{3x})'= (tan(x))'e^{3x}+tan(x)(e^{3x})'...

    Could you proceed from here...?
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  8. October 21st 2010, 09:37 AM #8
    Ackbeet
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    Well, technically, it's the product rule. But yes, that is the rule to use here. I was hoping Lil would see that on her own.
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  9. October 21st 2010, 09:45 AM #9
    Lil
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    Quote Originally Posted by Ackbeet View Post
    Well, technically, it's the product rule. But yes, that is the rule to use here. I was hoping Lil would see that on her own.
    ok, it's like (u\cdot v)'=u'v+uv'
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  10. October 21st 2010, 09:46 AM #10
    Ackbeet
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    Right.
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  11. October 21st 2010, 09:55 AM #11
    Lil
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    It's correct:
    (tan(x))'=\frac{1}{cos^2x}
    (e^{3x})'=e^{3x}*3
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  12. October 21st 2010, 09:56 AM #12
    Ackbeet
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    Correct. So you get what?
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  13. October 21st 2010, 10:00 AM #13
    Lil
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    =\frac{1}{cos^2x}\cdot e^{3x}+tgx\cdot e^{3x}\cdot 3

    What do next I don't know?
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  14. October 21st 2010, 10:01 AM #14
    Ackbeet
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    How about factoring out the e^{3x}?
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  15. October 21st 2010, 10:05 AM #15
    Lil
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    Quote Originally Posted by Ackbeet View Post
    How about factoring out the e^{3x}?
    3e^{3x}?
    How first e^{3x} I don't know
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