If , then…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If y=(tan⁡x)x2y=(\tan x)^{x^{2}}, then dydx\dfrac{dy}{dx} equals (a) (tan⁡x)x2(2xln⁡(tan⁡x)+x2sec⁡2x)(\tan x)^{x^{2}}\left(2x\ln(\tan x)+x^{2}\sec^{2}x\right) (b) (tan⁡x)x2(2xln⁡(tan⁡x)+x2sec⁡2xtan⁡x)(\tan x)^{x^{2}}\left(2x\ln(\tan x)+x^{2}\dfrac{\sec^{2}x}{\tan x}\right) (c) (tan⁡x)x2(x2sec⁡2xtan⁡x)(\tan x)^{x^{2}}\left(x^{2}\dfrac{\sec^{2}x}{\tan x}\right) (d) (tan⁡x)x2(2xln⁡(tan⁡x)+x2cot⁡x)(\tan x)^{x^{2}}\left(2x\ln(\tan x)+x^{2}\cot x\right)

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