What is the derivative of the function y=(2x-3)(sin(2x-3))?

To perform the differentiation, we'll have to apply the
product rule and the chain rule.

First, we'll apply the
product rule:

dy/dx = (2x-3)'*[sin(2x-3)] +
(2x-3)*[sin(2x-3)]'

Now, we'll apply the chain rule for the
term [sin(2x-3)]':

dy/dx = 2sin(2x-3) +
2(2x-3)*[cos(2x-3)]

We'll factorize by
2:

dy/dx = 2{sin(2x-3) +
(2x-3)*[cos(2x-3)]}

The derivative of the
given function is dy/dx = 2{sin(2x-3) +
(2x-3)*[cos(2x-3)]}.