Question

Find the derivative of the following functions not by 1st principle
(i) sin x cos x
(ii) sec x
(iv) cosec x
(v) 3cot x + 5 cosec x
(vi) 5sin x - 6 cos x + 7
(vii) 2 tan x-7 sec x


please solve these questions with formula. will be very helpful​

Answer 1

Answer:

d (sec x)/dx=-sec ^2thita(tan^2thita

Answer 2

Step-by-step explanation:

(i) sin x cos x

Ans.

= d/dx ( sin x cos x )

= sinx . d/dx ( cos x ) + cos x. d/dx ( sin x )

= sin x. ( - sin x ) + cos x . ( cos x )

= cos^2 x - sin^2 x

(ii) sec x

Ans.

= d/dx ( sec x )

= sec x . tan x

(iv) cosec x

Ans.

= d/dx ( cosec x )

= - cosec x . cot x

(v) 3cot x + 5 cosec x

Ans.

= d/dx ( 3cot x + 5 cosec x )

= 3 d/dx ( cot x ) + 5 d/dx ( cosec x )

= - 3 cosec^2 x - 5 cosec x . cot x

(vi) 5sin x - 6 cos x + 7

Ans.

= d/dx ( 5sin x - 6 cos x + 7 )

= 5 d/dx ( sin x ) - 6 d/dx ( cos x ) + d/dx ( 7 )

= 5 cos x - 6 ( - sin x ) + 0

= 5 cos x + 6 sin x

(vii) 2 tan x-7 sec x

Ans.

= d/dx ( 2 tan x - 7 sec x )

= 2 d/dx ( tan x ) - 7 d/dx ( sec x )

= 2 sec^2 x - 7 sec x . tan x