Find the derivative of y=3x^2Cos 2x

Answer 1

To find the derivative of y = 3x^2 * cos(2x), we'll use the product rule.

Let u = 3x^2 and v = cos(2x).

Now, let's find the derivative of u and v separately:

1. Finding the derivative of u:
u = 3x^2
du/dx = 2*3*x^(2-1) = 6x

2. Finding the derivative of v:
v = cos(2x)
dv/dx = -2*sin(2x) (Using the chain rule)

Now, we can use the product rule:

(dy/dx) = u*(dv/dx) + (du/dx)*v
(dy/dx) = 3x^2*(-2*sin(2x)) + 6x*cos(2x)
(dy/dx) = -6x^2*sin(2x) + 6x*cos(2x)

So, the derivative of y = 3x^2 * cos(2x) is dy/dx = -6x^2sin(2x) + 6xcos(2x).