Question

sin (ax +b)cos (cx+d)5.

Answer 1

The function that is to be differentiated is,

sin( ax+b ) cos( cx+d ) .

Differentiate the function with respect to x.

d dx ( sin( ax+b ) cos( cx+d ) )= ( cos( cx+d ) d dx ( sin( ax+b ) ) −sin( ax+b ) d dx ( cos( cx+d ) ) ) cos 2 ( cx+d ) = ( cos( cx+d )( cos( ax+b ) d dx ( ax+b ) ) −sin( ax+b )( −sin( cx+d ) d dx ( cx+d ) ) ) cos 2 ( cx+d ) = ( cos( cx+d )cos( ax+b )( d dx ( ax )+ d dx ( b ) ) +sin( ax+b )sin( cx+d )( d dx cx+ d dx b ) ) cos 2 ( cx+d ) = ( cos( cx+d )cos( ax+b )( a+0 )+sin( ax+b )sin( cx+d )( c+0 ) ) cos 2 ( cx+d )

Further solve the differentiation.

d dx ( sin( ax+b ) cos( cx+d ) )= ( acos( cx+d )cos( ax+b )+csin( ax+b )sin( cx+d ) ) cos 2 ( cx+d )