if `y=log_(sinx) tanx` then `((dy)/(dx)) _(pi/4)` is

Options

A. `(4)/(log 2)`
B. `-4 log 2`
C. `(-4)/( log 2)`
D. none of these

Explanation

To find the derivative of \( y = \log_{\sin x} (\tan x) \) and evaluate it at \( x = \frac{\pi}{4} \), we will follow these steps:

### Step 1: Change of Base Formula
Using the change of base formula for logarithms, we can rewrite \( y \):
\[ y = \frac{\log_{10}(\tan x)}{\log_{10}(\sin x)} \]

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