Ex 5.4, 9 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Finding derivative of Exponential & logarithm functions
Finding derivative of Exponential & logarithm functions
Last updated at April 16, 2024 by Teachoo
Ex 5.4, 9 Differentiate w.r.t. x in, cos𝑥/log𝑥 , x > 2Let 𝑦 = cos𝑥/log𝑥 Let 𝑢 = cos𝑥 & 𝑣 = log𝑥 ∴ 𝑦 = (.𝑢)/𝑣 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑦^′ = (𝑢/𝑣)^′ 𝑑𝑦/𝑑𝑥 = (𝑢^′ 𝑣 − 〖𝑣 〗^′ 𝑢)/𝑣^2 𝑑𝑦/𝑑𝑥 = ((cos𝑥 )^′ log𝑥 − (log𝑥 )^′ . 〖 cos〗𝑥)/(log𝑥 )^2 𝑑𝑦/𝑑𝑥 = (−sin𝑥 . log𝑥 − (1 )/𝑥 . 〖 cos〗𝑥)/(log𝑥 )^2 𝑑𝑦/𝑑𝑥 = (−(sin𝑥 . log𝑥 + (1 )/𝑥 . 〖 cos〗𝑥 ))/(log𝑥 )^2 𝑑𝑦/𝑑𝑥 = − (((𝑥 sin〖𝑥 log〖𝑥 + cos𝑥 〗 〗)/𝑥)/(log𝑥 )^2 ) 𝒅𝒚/𝒅𝒙 = − ((𝒙 𝒔𝒊𝒏〖𝒙 𝒍𝒐𝒈〖𝒙 +〖 𝒄𝒐𝒔〗𝒙 〗 〗)/(𝒙 (𝒍𝒐𝒈𝒙 )^𝟐 ))