Question

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

Answer 1

Let the given function be,

f( x )=( x+cosx )( x−tanx )

Differentiate the function with respect to x,

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

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