Question

Find derivative of (x^2+1)(2cosx+3sinx) with respect to x

Answer 1

Answer:

( 2 x ) ( 2 cos x + 3 sin x )  + ( x² + 1 ) ( 3 cos x - 2 sin x )

Step-by-step explanation:

Given :

f ( x ) = ( x² + 1 ) ( 2 cos x + 3 sin x )

We know :

( sin x )' = cos x

( cos x )' = sin x

Diff. w.r.t  x :

f' ( x ) = ( 2 cos x + 3 sin x ) ( x² + 1 )' + ( x² + 1 ) ( 2 cos x + 3 sin x )'

f' ( x ) = ( 2 cos x + 3 sin x ) ( 2 x + 0 ) + ( x² + 1 ) ( - 2 sin x + 3 cos x )

f' ( x ) = ( 2 cos x + 3 sin x ) ( 2 x ) + ( x² + 1 ) ( - 2 sin x + 3 cos x )

f' ( x ) = ( 2 x ) ( 2 cos x + 3 sin x )  + ( x² + 1 ) ( 3 cos x - 2 sin x )

Hence we get required answer!