What is the derivative of the function y2cos3x1sin3x1Solutio

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

Solution

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).