*x ^{n}* tan

*x*

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#### Solution

\[\text{ Let } u = x^n ; v = \tan x\]

\[\text{ Then }, u' = n x^{n - 1} ; v' = \sec^2 x\]

\[\text{ Using the product rule }:\]

\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]

\[\frac{d}{dx}\left( x^n \tan x \right) = x^n \sec^2 x + \tan x\left( n x^{n - 1} \right)\]

\[ = x^{n - 1} \left( x \sec^2 x + n \tan x \right)\]

Concept: The Concept of Derivative - Algebra of Derivative of Functions

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