Question

If f(a)=(sin a/l+cos a) square then f'(a) =​

Answer 1

Correct question :

If f ( a ) = ( sin a / 1 + cos a )² then f' ( a ) =​

Answer:

f' ( a ) = [ 2 sin a ( sin² a + cos² a + cos a ) ] / [ ( 1 + cos a )³ ]

Step-by-step explanation:

Given :

f ( a ) = ( sin a / 1 + cos a )²

Diff. w.r.t. a :

Using chain rule here :

We know :

( sin x )' = cos x

( cos x )' = - sin x

f' ( a ) = 2 ( sin a / 1 + cos a ) ( sin a / 1 + cos a )'

= > f' ( a ) = 2 ( sin a / 1 + cos a ) ( ( 1 + cos a ( sin a )' - sin a ( 1 + cos a )' ) / ( ( 1 + cos a )²

= > f' ( a ) = 2 ( sin a ) ( ( 1 + cos a ( cos a ) - sin a ( 1 + cos a )' ) / ( ( 1 + cos a )³

= >  f' ( a ) = 2 ( sin a ) ( ( 1 + cos a ( cos a ) - sin a ( 0 - sin a ) ) / ( 1 + cos a )³

= >  f' ( a ) = [ 2 ( sin a ) ( ( 1 + cos a ( cos a ) + sin a ( sin a ) ) ] / [ ( 1 + cos a )³ ]

= >  f' ( a ) = [ 2 ( sin a ) ( (  cos a + cos² a  + sin² a ) ] / [ (  1 + cos a )³ ]

= > f' ( a ) = [ 2 ( sin a ) ( ( sin² a + cos² a + cos a ) ] / [ ( 1 + cos a )³ ]

= >  f' ( a ) = [ 2 sin a ( sin² a + cos² a + cos a ) ] / [ ( 1 + cos a )³ ]

Hence we get required answer!