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Example 29 - Chapter 5 Class 12 Continuity and Differentiability - Part 3

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Example 29 Differentiate the following w.r.t. x: (iii) γ€–π‘π‘œπ‘ γ€—^(βˆ’1) "(ex)" Let 𝑦 = γ€–π‘π‘œπ‘ γ€—^(βˆ’1) "(ex)" Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑦/𝑑π‘₯ = 𝑑(cos^(βˆ’1)⁑(𝑒^π‘₯ ) )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = (βˆ’1)/√(1 βˆ’ (𝑒^π‘₯ )^2 ) . 𝑑(𝑒^π‘₯ )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = (βˆ’1)/√(1 βˆ’ (𝑒^π‘₯ )^2 ) . 𝑒^π‘₯ π’…π’š/𝒅𝒙 = (βˆ’π’†^𝒙)/√(𝟏 βˆ’ 𝒆^πŸπ’™ ) (As (cos^(βˆ’1)⁑π‘₯ )^β€²=(βˆ’1)/√(1 βˆ’ π‘₯^2 )) (As(𝑒^π‘₯ )^β€²=𝑒^π‘₯)

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