Ex 5.4, 10 - Class 12

Transcript

Ex 5.4, 10 Differentiate w.r.t. 𝑥 in, cos⁡(log⁡𝑥 + 𝑒﷮𝑥﷯), 𝑥 > 0 Let 𝑦 = cos﷮ log﷮𝑥﷯+ 𝑒﷮𝑥﷯﷯﷯ Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑 𝑦﷯﷮𝑑𝑥﷯ = 𝑑 cos﷮ log﷮𝑥﷯ + 𝑒﷮𝑥﷯﷯﷯﷯ ﷮𝑑𝑥﷯ 𝑑 𝑦﷯﷮𝑑𝑥﷯ = −sin ﷮ log﷮𝑥﷯+ 𝑒﷮𝑥﷯﷯﷯ 𝑑 log﷮𝑥﷯ + 𝑒﷮𝑥﷯﷯﷮𝑑𝑥﷯ 𝑑 𝑦﷯﷮𝑑𝑥﷯ = −sin ﷮ log﷮𝑥﷯+ 𝑒﷮𝑥﷯﷯﷯ 𝑑 log﷮𝑥﷯﷯ ﷮𝑑𝑥﷯ + 𝑑 𝑒﷮𝑥﷯﷯﷮𝑑𝑥﷯﷯ 𝑑 𝑦﷯﷮𝑑𝑥﷯ = − sin ﷮ log﷮𝑥﷯+ 𝑒﷮𝑥﷯﷯﷯ 1﷮𝑥﷯ + 𝑒﷮𝑥﷯﷯ 𝒅 𝒚﷯﷮𝒅𝒙﷯ = −﷮ 𝟏﷮𝒙﷯ + 𝒆﷮𝒙﷯﷯﷯ 𝐬𝐢𝐧 𝒍𝒐𝒈﷮𝒙﷯ + 𝒆﷮𝒙﷯﷯