Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Xn Tan X - Mathematics

xn tan 

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Solution

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

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.4 | Q 4 | Page 39
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