# Thread: Help with this logarithmic differentiation problem?

1. ## 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?

$\displaystyle 5^{sin(x)}+sin^5(x)$

2. Originally Posted by Mattpd
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?

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

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

$\displaystyle \frac{dy}{dx} = 5^{\sin{x}} \cdot \cos{x} \cdot \ln{5} + 5(\sin{x})^4 \cdot \cos{x}$

3. So because 5 is being raised to something complicated, you can't just use the power rule, you have to use this rule?

4. Originally Posted by Mattpd
So because 5 is being raised to something complicated, you can't just use the power rule, you have to use this rule?
yes