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Question and Answer

Differentiate the following function with respect to x.
\(x^n\tan x\).

(A) \(x^{n-1}(n \tan x+x\sec x)\).
(B) \(x^{n-1}(n \tan x+x\sec^2x)\).
(C) \(x^{n-1}(n \tan x+\sec^2x)\).
(D) \(x^{n-1}(n \tan x+x\sec^{-2}x)\).

Answer

Answer: B
Given expression

\(x^n \tan x\)

differentiating w.r.t. \(x\), we get

\( \dfrac d{dx}(x^n \tan x)\)

\(=\dfrac d{dx}(x^n)\tan x +x^n \dfrac d{dx}\tan x\)

\(=nx^{n-1}\tan x+ x^n \sec ^2 x\)

\(= x^{n-1}(n\tan x+x\sec ^2 x)\)
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