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

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### 2 Answers

We have to find the derivative of y=(2x-3)(sin(2x-3))

y' = [(2x-3)(sin(2x-3))]'

use the product rule

=> y' = (2x - 3)'* sin(2x - 3) + (2x - 3)*(sin(2x - 3))'

=> y' = 2*sin(2x - 3) + (2x - 3)*2*cos(2x - 3)

=> y' = 2*sin(2x - 3) + (4x - 6)cos(2x - 3)

**The required derivative is 2*sin(2x - 3) + (4x - 6)cos(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)]}.**