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Ex 5.4, 1 Differentiate 𝑀.π‘Ÿ.𝑑. π‘₯ in , 𝑒^π‘₯/sin⁑π‘₯ Let π’š = 𝑒^π‘₯/sin⁑π‘₯ Let 𝑒 =𝑒^π‘₯ & 𝑣 = sin⁑π‘₯ ∴ π’š = 𝒖/𝒗 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑(𝑦)/𝑑π‘₯ = 𝑑(𝑒/𝑣)/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = ((𝑒)^β€² 𝑣 βˆ’ 〖𝑣 γ€—^β€² 𝑒)/𝑣^2 𝑑𝑦/𝑑π‘₯ = ((𝑒)^β€² 𝑣 βˆ’ 〖𝑣 γ€—^β€² 𝑒)/𝑣^2 π’…π’š/𝒅𝒙 = (𝒅(𝒆^𝒙 )/𝒅𝒙 . π’”π’Šπ’β‘π’™ βˆ’ (𝒅(π’”π’Šπ’β‘π’™ ) )/𝒅𝒙 . 𝒆^𝒙)/(π’”π’Šπ’β‘π’™ )^𝟐 𝑑𝑦/𝑑π‘₯ = (𝑒^π‘₯ . sin⁑π‘₯ βˆ’ cos⁑π‘₯ . 𝑒^π‘₯)/(sin⁑π‘₯ )^2 𝑑𝑦/𝑑π‘₯ = (𝑒^π‘₯ (sin⁑π‘₯ βˆ’ cos⁑π‘₯ ))/(sin⁑π‘₯ )^2 π’…π’š/𝒅𝒙 = (𝒆^𝒙 (π’”π’Šπ’β‘π’™ βˆ’ 𝒄𝒐𝒔⁑𝒙 ))/γ€–π’”π’Šπ’γ€—^πŸβ‘π’™

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.