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Math Help - Help with this logarithmic differentiation problem?

  1. #1
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    Help with this logarithmic differentiation problem?

    I have a final coming up and I am a little rusty on the things we did early in the class. I already have this problem worked out so no need to do that unless you want to. I see that they introduced ln into the equation, but I don't quite remember how it all works. Can you refresh my memory?

    5^{sin(x)}+sin^5(x)
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  2. #2
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    Quote Originally Posted by Mattpd View Post
    I have a final coming up and I am a little rusty on the things we did early in the class. I already have this problem worked out so no need to do that unless you want to. I see that they introduced ln into the equation, but I don't quite remember how it all works. Can you refresh my memory?

    5^{sin(x)}+sin^5(x)
    note that \frac{d}{dx} a^u = a^u \cdot \frac{du}{dx} \cdot \ln{a}

    y = 5^{\sin{x}} + (\sin{x})^5

    \frac{dy}{dx} = 5^{\sin{x}} \cdot \cos{x} \cdot \ln{5} + 5(\sin{x})^4 \cdot \cos{x}
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  3. #3
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    So because 5 is being raised to something complicated, you can't just use the power rule, you have to use this rule?
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  4. #4
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    Quote Originally Posted by Mattpd View Post
    So because 5 is being raised to something complicated, you can't just use the power rule, you have to use this rule?
    yes
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