Check sibling questions

Slide14.jpeg

Slide15.jpeg

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Ex 5.4, 9 Differentiate w.r.t. x in, cos⁑π‘₯/log⁑π‘₯ , x > 2Let 𝑦 = cos⁑π‘₯/log⁑π‘₯ Let 𝑒 = cos⁑π‘₯ & 𝑣 = log⁑π‘₯ ∴ 𝑦 = (.𝑒)/𝑣 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑦^β€² = (𝑒/𝑣)^β€² 𝑑𝑦/𝑑π‘₯ = (𝑒^β€² 𝑣 βˆ’ 〖𝑣 γ€—^β€² 𝑒)/𝑣^2 𝑑𝑦/𝑑π‘₯ = ((cos⁑π‘₯ )^β€² log⁑π‘₯ βˆ’ (log⁑π‘₯ )^β€² . γ€– cos〗⁑π‘₯)/(log⁑π‘₯ )^2 𝑑𝑦/𝑑π‘₯ = (βˆ’sin⁑π‘₯ . log⁑π‘₯ βˆ’ (1 )/π‘₯ . γ€– cos〗⁑π‘₯)/(log⁑π‘₯ )^2 𝑑𝑦/𝑑π‘₯ = (βˆ’(sin⁑π‘₯ . log⁑π‘₯ + (1 )/π‘₯ . γ€– cos〗⁑π‘₯ ))/(log⁑π‘₯ )^2 𝑑𝑦/𝑑π‘₯ = βˆ’ (((π‘₯ sin⁑〖π‘₯ log⁑〖π‘₯ + cos⁑π‘₯ γ€— γ€—)/π‘₯)/(log⁑π‘₯ )^2 ) π’…π’š/𝒅𝒙 = βˆ’ ((𝒙 π’”π’Šπ’β‘γ€–π’™ π’π’π’ˆβ‘γ€–π’™ +γ€– 𝒄𝒐𝒔〗⁑𝒙 γ€— γ€—)/(𝒙 (π’π’π’ˆβ‘π’™ )^𝟐 ))

Davneet Singh's photo - Co-founder, Teachoo

Made by

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.