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Math Help - Calculate f'(x)

  1. #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. #2
    A Plied Mathematician
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    Are t and g considered constant?
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  3. #3
    Lil
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    It's tg(x)
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    A Plied Mathematician
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    Is that the tangent function, then?
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  5. #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. #6
    A Plied Mathematician
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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. #7
    MHF Contributor Also sprach Zarathustra's Avatar
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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. #8
    A Plied Mathematician
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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. #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. #10
    A Plied Mathematician
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    Right.
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  11. #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. #12
    A Plied Mathematician
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    Correct. So you get what?
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  13. #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. #14
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    How about factoring out the e^{3x}?
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  15. #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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