Help with this logarithmic differentiation problem?

• May 5th 2010, 04:37 PM
Mattpd
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?

$5^{sin(x)}+sin^5(x)$
• May 5th 2010, 04:53 PM
skeeter
Quote:

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?

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

note that $\frac{d}{dx} a^u = a^u \cdot \frac{du}{dx} \cdot \ln{a}$

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

$\frac{dy}{dx} = 5^{\sin{x}} \cdot \cos{x} \cdot \ln{5} + 5(\sin{x})^4 \cdot \cos{x}$
• May 5th 2010, 05:17 PM
Mattpd
So because 5 is being raised to something complicated, you can't just use the power rule, you have to use this rule?
• May 5th 2010, 05:19 PM
skeeter
Quote:

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