Ex 5.4, 4

Transcript

Ex 5.4, 4 Differentiate 𝑤.𝑟.𝑡. 𝑥 in , sin﷮ tan﷮−1﷯ 𝑒﷮−𝑥﷯﷯﷯ Let 𝑦 = sin﷮ tan﷮−1﷯ 𝑒﷮−𝑥﷯﷯﷯ Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑 𝑦﷯﷮𝑑𝑥﷯ = 𝑑 sin﷮ tan﷮−1﷯ 𝑒﷮−𝑥﷯﷯﷯﷯﷮𝑑𝑥﷯ = cos ﷮ tan﷮−1﷯ 𝑒﷮−𝑥﷯﷯﷯ × 𝑑 tan﷮−1﷯ 𝑒﷮−𝑥﷯﷯﷮𝑑𝑥﷯ = cos ﷮ tan﷮−1﷯ 𝑒﷮−𝑥﷯﷯﷯ × 1﷮1 + 𝑒﷮−𝑥﷯﷯﷮2﷯ ﷯ × 𝑑 𝑒﷮−𝑥﷯﷯﷮𝑑𝑥﷯ = cos ﷮ tan﷮−1﷯ 𝑒﷮−𝑥﷯﷯﷯ × 1﷮1 + 𝑒﷮−𝑥﷯﷯﷮2﷯ ﷯ × 𝑒﷮−𝑥﷯ = 𝑒﷮−𝑥﷯ cos ﷮ tan﷮−1﷯ 𝑒﷮−𝑥﷯﷯﷯﷮1 + 𝑒﷮−𝑥﷯﷯﷮2﷯ ﷯ = − 𝒆﷮−𝒙﷯ 𝐜𝐨𝐬 ﷮ 𝒕𝒂𝒏﷮−𝟏﷯ 𝒆﷮−𝒙﷯﷯﷯﷮𝟏 + 𝒆﷮−𝟐𝒙﷯ ﷯