Question

ax+bcx+d5.

Answer 1

Consider the function,

f( x )= ax+b cx+d

The quotient rule of derivative to find the derivative of the function is,

d dx ( U V )= ( U V ′ −V U ′ ) V 2

Where U ′ and V ′ are the derivative of their respective functions.

Apply quotient rule of derivative in the given function,

f ′ ( x )= ( cx+d ) d dx ( ax+b )−( ax+b ) d dx ( cx+d ) ( cx+d ) 2 = ( cx+d )a d dx x−( ax+b )c d dx x ( cx+d ) 2 = ( cx+d )a−( ax+b )c ( cx+d ) 2

Further simplify,

f ′ ( x )= ( acx+ad−acx−bc ) ( cx+d ) 2 = ad−bc ( cx+d ) 2

Thus, the derivative of ax+b cx+d is ad−bc ( cx+d ) 2 .