Ex 5.3, 3 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Chapter 5 Class 12 Continuity and Differentiability
Concept wise
- Checking continuity at a given point
- Checking continuity at any point
- Checking continuity using LHL and RHL
- Algebra of continous functions
- Continuity of composite functions
- Checking if funciton is differentiable
- Finding derivative of a function by chain rule
-
Finding derivative of Implicit functions
- Finding derivative of Inverse trigonometric functions
- Finding derivative of Exponential & logarithm functions
- Logarithmic Differentiation - Type 1
- Logarithmic Differentiation - Type 2
- Derivatives in parametric form
- Finding second order derivatives - Normal form
- Finding second order derivatives- Implicit form
- Proofs
- Verify Rolles theorem
- Verify Mean Value Theorem
Transcript
Ex 5.3, 3 Find 𝑑𝑦/𝑑𝑥 in, 𝑎𝑥 + 𝑏𝑦2 = cos𝑦 𝑎𝑥 + 𝑏𝑦2 = cos𝑦 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑(𝑎𝑥 + 𝑏𝑦2)/𝑑𝑥 = (𝑑 (c𝑜𝑠𝑦 ))/𝑑𝑥 𝑑(𝑎𝑥)/𝑑𝑥 +𝑑(𝑏𝑦2)/𝑑𝑥= (𝑑 〖(cos〗𝑦))/𝑑𝑥 a 𝑑𝑥/𝑑𝑥 +𝑏 𝑑(𝑦2)/𝑑𝑥= (𝑑 )/𝑑𝑥 cos y a + b (𝑑 (𝑦2))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦= (𝑑 (cos𝑦 ))/𝑑𝑥 ×𝑑𝑦/𝑑𝑦 a + b (𝑑 (𝑦2))/𝑑𝑦 × 𝑑𝑦/𝑑𝑥= (𝑑 (cos𝑦 ))/𝑑𝑦 ×𝑑𝑦/𝑑𝑥 𝑎 + 𝑏 .2𝑦× 𝑑𝑦/𝑑𝑥= −sin〖𝑦 〗 𝑑𝑦/𝑑𝑥 𝑎 + 2𝑏𝑦 . 𝑑𝑦/𝑑𝑥= −sin〖𝑦 〗 𝑑𝑦/𝑑𝑥 2𝑏𝑦 . 𝑑𝑦/𝑑𝑥 + sin〖𝑦 〗 𝑑𝑦/𝑑𝑥 = 0 − 𝑎 𝑑𝑦/𝑑𝑥 (2𝑏𝑦 + sin〖𝑦 〗) = −𝑎 𝒅𝒚/𝒅𝒙 = (−𝒂)/(𝟐𝒃𝒚 " + " 𝒔𝒊𝒏〖𝒚 〗 )
