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Question
log3 x + 3 loge x + 2 tan x
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Solution
\[\frac{d}{dx}\left( \log_3 x + 3 \log_e x + 2 \tan x \right)\]
\[ = \frac{d}{dx}\left( \frac{\log x}{\log 3} \right) + 3\frac{d}{dx}\left( \log_e x \right) + 2\frac{d}{dx}\left( \tan x \right)\]
\[ = \frac{1}{\log 3} . \frac{1}{x} + 3 . \frac{1}{x} + 2 \sec^2 x\]
\[ = \frac{1}{x \log 3} + \frac{3}{x} + 2 \sec^2 x\]
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