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Thread: Derivative ae^(b theta)

  1. #1
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    Derivative ae^(b theta)

    Good afternoon,

    What is the method fo differentiating the following:

     <br />
\displaystyle ae^{b\theta}<br />

    Is it as simple as...

     <br />
\displaystyle abe^{b\theta}<br />

    I was looking for an explanation of the rules involved with this particular situation, but could not find what I was looking for.
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  2. #2
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    Forgot...

    The a and b are positive constants. So, I would assume that would make my guess as to the answer correct.
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  3. #3
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    Quote Originally Posted by MechEng View Post
    Good afternoon,

    What is the method fo differentiating the following:

     <br />
\displaystyle ae^{b\theta}<br />

    Is it as simple as...

     <br />
\displaystyle abe^{b\theta}<br />

    I was looking for an explanation of the rules involved with this particular situation, but could not find what I was looking for.
    The chain rule

    f(x)=ae^{x} and x=b\theta

    The chain rule gives

    \displaystyle \frac{df}{d\theta}=\frac{df}{dx}\frac{dx}{d\theta}  =ae^{x}b=abe^{b\theta}
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  4. #4
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    That's what I was thinking... I've been second guessing myself too much.

    Thank you!
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