Differentiate the following with respect of `x :(log)_3x+3(log)_e x+2tanx`

Explanation

`therefore` `frac{d}{dx}{f(x)}=frac{d}{dx}(log _{3} x+3 log _{e} x+2 tan x)`

`Rightarrow f^{prime}(x)=frac{d}{d x}(log _{3} x) +3 frac{d}{d x}(log _{e} x) `
`+2 frac{d}{d x}(tan x)`

Use the formula: `frac{d}{d x}(log _{a} x)`

`=frac{1}{x log _{e} a}` and `frac{d}{d x}(tan x)`

`=sec ^{2} x`

`therefore f^{prime}(x)=frac{1}{x log _{e} 3}+frac{3}{x log _{e} e}+2 sec ^{2} x`

`Rightarrow f^{prime}(x)=frac{1}{x log _{e^{3}}}+frac{3}{x}+2 sec ^{2} x`

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