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Question
xn tan x
Solution
\[\text{ Let } u = x^n ; v = \tan x\]
\[\text{ Then }, u' = n x^{n - 1} ; v' = \sec^2 x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( x^n \tan x \right) = x^n \sec^2 x + \tan x\left( n x^{n - 1} \right)\]
\[ = x^{n - 1} \left( x \sec^2 x + n \tan x \right)\]
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