Question

Find the second derivative of y=2cos(x/2).

A) −sin(x/2)

B) cos(x/2)

C) sin(x/2)

D) −cos(x/2)

Answer 1

The second derivative of y=2cos(x/2) is cos(x/2).

Step-by-step explanation:

To find the second derivative of y=2cos(x/2), we need to find the derivative of y with respect to x first, and then take the derivative of that result. Let's start by finding the first derivative:

dy/dx = d/dx(2cos(x/2))

Using the chain rule, the derivative of cos(x/2) is -sin(x/2), so:

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

Now, to find the second derivative, we take the derivative of -2sin(x/2):

d^2y/dx^2 = d/dx(-2sin(x/2))

Again using the chain rule, the derivative of -sin(x/2) is -(-cos(x/2)) = cos(x/2).

So, the second derivative of y is cos(x/2).