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Math Help - Derivatives cont'd...

  1. #1
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    Derivatives cont'd...

    I have another derivative question, this one's a little more complicated...

    Find the derivative of the following:

    h(x) = 3e^((sin)(x+2))

    I'm having a hard time even getting started on this one...
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  2. #2
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    Quote Originally Posted by Jools View Post
    I have another derivative question, this one's a little more complicated...

    Find the derivative of the following:

    h(x) = 3e^((sin)(x+2))

    I'm having a hard time even getting started on this one...
    This is precalc? Wow. We didn't even touch derivatives when I took it. Good luck...
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  3. #3
    Member mathemagister's Avatar
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    Quote Originally Posted by Jools View Post
    I have another derivative question, this one's a little more complicated...

    Find the derivative of the following:

    h(x) = 3e^((sin)(x+2))

    I'm having a hard time even getting started on this one...
    What do you mean by (sin)(x+2)? Do you mean:

    h(x) = 3e^{\sin(x+2)}

    Using the chain rule: the derivative of e^{f(x)} is e^{f(x)} \cdot f'(x)

    h'(x) = 3e^{\sin(x+2)} \cdot \cos(x+2) \cdot 1 = 3 \cos(x+2) e^{\sin(x+2)}
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  4. #4
    Member mathemagister's Avatar
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    Quote Originally Posted by Jools View Post
    I have another derivative question, this one's a little more complicated...

    Find the derivative of the following:

    h(x) = 3e^((sin)(x+2))

    I'm having a hard time even getting started on this one...
    In case you meant:

    h(x) = 3e^{(\sin{x})(x+2)}

    Then, using the same method I did before and the product rule:

    h'(x) = 3e^{(\sin{x})(x+2)} [(\sin{x}) + (x+2)\cos{x}]

    Do you understand it now?
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  5. #5
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    Thank you! I do... There's just so many varaitions of the chain rule, I have a hard time determining which one to use... I guess practise will be the key.
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  6. #6
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    There is only one chain rule- applied to many different functions.
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