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Last updated at Jan. 16, 2020 by Teachoo

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Find the derivative of f given by f (x) = cos–1 𝑥 assuming it exists. Let y = cos–1 𝑥 cos𝑦= 𝑥 𝑥 =cos𝑦 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 (𝑑(𝑥))/𝑑𝑥 = (𝑑 (cos𝑦 ))/𝑑𝑥 1 = (𝑑 (cos𝑦 ))/𝑑𝑥 We need 𝑑𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (cos𝑦 ))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦 1 = −sin𝑦 . 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/(− 𝒔𝒊𝒏𝒚) 𝑑𝑦/𝑑𝑥 = (−1)/(√(𝟏 − 〖𝒄𝒐𝒔〗^𝟐𝒚 ) " " ) We know that sin2 𝑦 + cos2 𝑦 = 1 sin2 𝑦 = 1 − cos2 𝑦 sin 𝑦 = √(1−cos^2𝑦 ) Putting value of 𝑐𝑜𝑠𝑦 = 𝑥 𝑑𝑦/𝑑𝑥 = (−1)/(√(1 − 𝒙^𝟐 ) " " ) As 𝑦 = cos^(−1) 𝑥 So, 𝑐𝑜𝑠𝑦 = 𝑥 Hence, (𝒅(〖𝒄𝒐𝒔〗^(−𝟏)〖𝒙)〗)/𝒅𝒙 = (−1)/(√(1 − 𝒙^𝟐 ) " " )

Finding derivative of Inverse trigonometric functions

Derivative of cos-1 x (Cos inverse x)
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Example 26 Important

Example 27

Derivative of cot-1 x (cot inverse x)

Derivative of sec-1 x (Sec inverse x)

Derivative of cosec-1 x (Cosec inverse x)

Ex 5.3, 14

Ex 5.3, 9 Important

Ex 5.3, 13 Important

Ex 5.3, 12 Important

Ex 5.3, 11 Important

Ex 5.3, 10 Important

Ex 5.3, 15 Important

Misc 5 Important

Misc 4

Misc 13 Important

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.