please any body help me

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- Jul 26th 2006, 09:04 AMm777please help me to solve that questions
please any body help me

- Jul 26th 2006, 12:04 PMgalactus
For #3, I'd try the ratio test. It works well with factorials and powers.

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

Try logarithmic differentiation.

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

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

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

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

Differentiate:

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

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

$\displaystyle y'=cos(x)3^{sin(x)}ln(3)$ - Jul 26th 2006, 12:23 PMThePerfectHacker
You can also use a useful rule.

$\displaystyle y=a^{f(x)}$ where $\displaystyle a>0$ and $\displaystyle f(x)$ is some function of "x" then,

$\displaystyle y'=\ln a f'(x) a^{f(x)}$

When used with your problem gives the same result as galactus said.