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Question

25. (x +cosx) (x- tanx)

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Solution

Let the given function be,

f( x )=( x+cosx )( xtanx )

Differentiate the function with respect to x,

f ( x )=( x+cosx ) d dx ( xtanx )+( xtanx ) d dx ( x+cosx ) =( x+cosx )[ d dx x d dx tanx ]+( xtanx )[ d dx x+ d dx cosx ] =( x+cosx )( 1 sec 2 x )+( xtanx )( 1sinx ) = tan 2 x( x+cosx )+( xtanx )( 1sinx )

Therefore, the derivative of the given function is tan 2 x( x+cosx )+( xtanx )( 1sinx ).


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