Question

Differentiate the function w.r.t.x:
$\rm \log_{3}x - 3\log_{e} x + 2\tan x$

Answer 1

HOPE IT HELPS U ✌️✌️

Answer 2

We know that from the properties of Logarithmic,we can write

$\log_{3}x = \frac{ log_{e}(x) }{ log_{e}(3) }$
and now all the expression are differentiable,so apply formula

$\frac{d}{dx}( \log_{3}x - 3\log_{e} x + 2\tan \: x) \\ \\ = > \frac{d}{dx}\frac{ log_{e}(x) }{ log_{e}(3) } - \frac{d}{dx} (3\log_{e} x ) + 2 \frac{d}{dx} (tan \: x) \\ \\ = \frac{1}{ log_{e}(3) } \frac{d( log_{e}x) }{dx} -3 \frac{d}{dx} (\log_{e} x ) + 2 \frac{d}{dx} (tan \: x) \\ \\ = \frac{1}{ log_{e}(3) } \times \frac{1}{x} -3 \frac{1}{x} + 2 {sec}^{2} x \\ \\ \frac{d}{dx}( \log_{3}x - 3\log_{e} x + 2\tan \: x) = \\\\\frac{1}{x \: log_{e}(3) } + \frac{3}{x} + 2 {sec}^{2} x$


Hope it helps you.