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Math Help - find f'(x)

  1. #1
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    find f'(x)

    this is a little confusing

    f(x) = e^xsinx

    i don't know what rule to use with this
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  2. #2
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    Which is true?

    1. f(x) = e^x \sin x

    2. f(x) = e^{x \sin x}
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  3. #3
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    f'(x)= sin(x) d(e^x)/dx + e^x * d(sin(x))/dx
    f'(x)= e^x * (sin(x) + cos(x))
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  4. #4
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    number 2 is it icemanfan
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  5. #5
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    not 100% certain but i think it might be lnx^(sin-1)x does that sound right to you?
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  6. #6
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    im not sure. im lost even more just by looking at my notes.
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  7. #7
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    ahh i read it wrong anyways lol ignore that
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  8. #8
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    Quote Originally Posted by uniquereason81 View Post
    number 2 is it icemanfan
    Then use the chain rule.

    \frac{d}{dx} e^u = e^u \frac{du}{dx}

    Hence:
    f'(x) = e^{x \sin x} \left(\frac{d}{dx} x \sin x \right)

    Applying the product rule to the leftover derivative:
    f'(x) = e^{x \sin x} (x \cos x + \sin x)
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  9. #9
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    Can u tell me the product rule i can't find it in my notes
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  10. #10
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    Quote Originally Posted by uniquereason81 View Post
    Can u tell me the product rule i can't find it in my notes
    If f(x) = g(x) \cdot h(x), then:

    f'(x) = g(x) \cdot h'(x) + h(x) \cdot g'(x)
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  11. #11
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    its different though when you have e^u right
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  12. #12
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    Quote Originally Posted by uniquereason81 View Post
    its different though when you have e^u right
    The product rule does not change based on situations. In your example, u was a function of x, which prompted us to use the chain rule to evaluate the derivative. The fact that du/dx required us to use the product rule was a function (pardon the pun) of the function u(x) = x \sin x.
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  13. #13
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    not to be an ass but can you take it a little further with the problem because im so confuse and i have to know this by friday
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  14. #14
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    Okay. Let me ask a simpler question. How would you evaluate the derivative of f(x) = e^{3x^2}?
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  15. #15
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    e^3x^2 * 6x
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