24. (ax2 + sinx)(p+ qcosx)

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Solution

Let the given function be,

f( x )=( a x 2 +sinx )( p+qcosx )

Differentiate the function with respect to x,

f ′ ( x )=( a x 2 +sinx ) d dx ( p+qcosx )+( p+qcosx ) d dx ( a x 2 +sinx ) =( a x 2 +sinx )[ q( −sinx ) ]+( p+qcosx )( a( 2x )+cosx ) =( a x 2 +sinx )( −qsinx )+( p+qcosx )( 2ax+cosx )

Therefore, the derivative of the given function is ( a x 2 +sinx )( −qsinx )+( p+qcosx )( 2ax+cosx ).

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