• July 26th 2006, 09:04 AM
m777
• July 26th 2006, 12:04 PM
galactus
For #3, I'd try the ratio test. It works well with factorials and powers.

For #1, can you find the derivative of $3^{sin({\theta})}$?.

Try logarithmic differentiation.

I'll use x instead of theta for the sake of typing.

$y=3^{sin(x)}$

$ln(y)=ln(3^{sin(x)})$

$ln(y)=sin(x)ln(3)$

Differentiate:

$\frac{y'}{y}=cos(x)ln(3)$

Remember, $y=3^{sin(x)}$

$y'=cos(x)3^{sin(x)}ln(3)$
• July 26th 2006, 12:23 PM
ThePerfectHacker
You can also use a useful rule.
$y=a^{f(x)}$ where $a>0$ and $f(x)$ is some function of "x" then,
$y'=\ln a f'(x) a^{f(x)}$
When used with your problem gives the same result as galactus said.