What is the derivative of the function y=2cos(3x-1)*sin(3x-1)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The given function f(x) = 2*cos (3x-1)*sin(3x-1)

Use the product rule and chain rule to find the derivative.

f'(x) = 2*[cos (3x-1)]'*sin(3x-1) + 2*cos (3x-1)*[sin(3x-1)]'

=> 2*3*(-sin (3x - 1)*sin (3x - 1) + 2*cos (3x - 1)*3*sin (3x - 1)

=> 6[ (cos (3x - 1))^2 - (sin (3x - 1))^2]

=> 6*cos 2*(3x - 1)

=> 6*cos (6x - 2)

The derivative of the given function is 6*cos (6x - 2)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We recognize the formula of the double angle in the given expresison of the function:

y = 2 sin (3x-1)*cos (3x - 1)

y = sin 2*(3x-1)

y = sin (6x - 2)

Since the function to be differentiated is the result of composition of two functions, we'll use the chain rule to detemrine the first derivative of the function.

We'll differentiate with respect to x:

dy/dx = [cos (6x - 2)]*(6x - 2)'

dy/dx = 6*cos(6x - 2)

The first derivative of the given function is: dy/dx = 6*cos(6x - 2).

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