Find the derivative of cos x from first principle.

Solution:

f’(x) = limh→ 0 [f(x+h) – f(x)]/h

= limh→ 0 [cos (x+h) – cos x]/h

= limh→ 0[cos x cos h – sin x sin h – cos x]/h

= limh → 0 [- cos x(1-cos h) – sin x sin h]/h

= limh → 0 [- cos x(1-cos h)/h – [sin x sin h)/h]

= -cos x limh → 0(1-cos h)/h – sin x limh → 0sin h/h

= – cos x . 0 – sin x (1)

= – sin x

Hence the derivative of cos x is -sin x.

Was this answer helpful?

 
   

0 (0)

(0)
(0)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class

Ask
Question