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$$y = \log_7(e^{-x}\cos\pi x)$$

I got: $$y' = \frac {-\sin\pi xe^{-x} - \cos\pi x e^{-x}}{e^{-x}\cos\pi x\ln(7)}$$

Is that correct?

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In general, the derivative of $\log_a y$, where $y$ is a function of $x$, is

$$\frac{y'}{y \ln a},$$

which I believe you know.

You dropped a $\pi$ when you took the derivative of $\cos (\pi x)$. The derivative is $-\pi \sin(\pi x)$ by the chain rule. Other than that, looks good.

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Where did I drop the $\pi$? – dsta Oct 21 '12 at 2:21
Ok, thank you! I appreciate it. – dsta Oct 21 '12 at 2:24
@dsta No problem, glad to help. It's nice that you had already made an attempt and showed what you got. You're not just trying to get someone to do your homework, but to actually learn! – Graphth Oct 21 '12 at 2:40

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