23, x2 +1 cos x

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Solution

Let the given function be,

f( x )=( x 2 +1 )cosx

Differentiate the function with respect to x,

f ′ ( x )=( x 2 +1 ) d dx cosx+cosx d dx ( x 2 +1 ) =( x 2 +1 )( −sinx )+cosx[ d dx x 2 + d dx 1 ] =( x 2 +1 )( −sinx )+cosx( 2x+0 ) =− x 2 sinx−sinx+2xcosx

Therefore, the derivative of the given function is − x 2 sinx−sinx+2xcosx.

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