Question

Y=cos(2x) find the derivative when (d^(3)y)/(dx^(3))

Answer 1

To find the third derivative of y = cos(2x), we'll first find the first derivative and then successively take the derivatives until we reach the third derivative.

1. First derivative (dy/dx):

y = cos(2x)

dy/dx = -2sin(2x)

2. Second derivative (d^2y/dx^2):

d(dy/dx)/dx = d(-2sin(2x))/dx

d^2y/dx^2 = -4cos(2x)

3. Third derivative (d^3y/dx^3):

d(d^2y/dx^2)/dx = d(-4cos(2x))/dx

d^3y/dx^3 = 8sin(2x)

So, the third derivative of y = cos(2x) is d^3y/dx^3 = 8sin(2x).

Explanation: