# Differentiate the function.

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

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
$$\frac{y'}{y \ln a},$$
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.
Where did I drop the $\pi$? – dsta Oct 21 '12 at 2:21