# Ex 5.4, 10 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Sept. 17, 2019 by Teachoo

Last updated at Sept. 17, 2019 by Teachoo

Transcript

Ex 5.4, 10 Differentiate w.r.t. 𝑥 in, cos(log𝑥 + 𝑒𝑥), 𝑥 > 0 Let 𝑦 = cos log𝑥+ 𝑒𝑥 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑 𝑦𝑑𝑥 = 𝑑 cos log𝑥 + 𝑒𝑥 𝑑𝑥 𝑑 𝑦𝑑𝑥 = −sin log𝑥+ 𝑒𝑥 𝑑 log𝑥 + 𝑒𝑥𝑑𝑥 𝑑 𝑦𝑑𝑥 = −sin log𝑥+ 𝑒𝑥 𝑑 log𝑥 𝑑𝑥 + 𝑑 𝑒𝑥𝑑𝑥 𝑑 𝑦𝑑𝑥 = − sin log𝑥+ 𝑒𝑥 1𝑥 + 𝑒𝑥 𝒅 𝒚𝒅𝒙 = − 𝟏𝒙 + 𝒆𝒙 𝐬𝐢𝐧 𝒍𝒐𝒈𝒙 + 𝒆𝒙

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