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Ex 5.2, 4 - Differentiate sec (tan (root x)) - Class 12 - Ex 5.2

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Ex 5.2, 4 Differentiate the functions with respect to x sec (tan ( √π‘₯ )) Let 𝑦 = sec (tan √π‘₯ ) We need to find Derivative of 𝑦 i.e. 𝑦’ = (sec⁑〖〖(tanγ€—β‘βˆšπ‘₯)γ€— )^β€² = γ€–π¬πžπœ 〗⁑〖(π­πšπ§β‘βˆšπ’™)γ€— γ€–π­πšπ§ 〗⁑〖(π’•π’‚π’β‘βˆšπ’™)γ€— (tan⁑√π‘₯ )^β€² = γ€–sec 〗⁑〖(tan⁑√π‘₯)γ€— γ€–tan 〗⁑〖(tan⁑√π‘₯)γ€—. ("sec2 " √π‘₯ " . " (√π‘₯)^β€²) = γ€–sec 〗⁑〖(tan⁑√π‘₯)γ€— γ€–tan 〗⁑〖(tan⁑√π‘₯)γ€—. sec2 " " √π‘₯ Γ— 1/(2√π‘₯) = (𝒔𝒆𝒄⁑〖(π’•π’‚π’β‘βˆšπ’™ γ€—)𝒔𝒆𝒄⁑〖(π’•π’‚π’β‘βˆšπ’™ γ€—)〖𝒔𝒆𝒄〗^πŸβ‘βˆšπ’™ )/(πŸβˆšπ’™)

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