Question

if y=2cos(x/2) then d^2y/dx^2 =

Answer 1

We first need dy/dx.

dy/dx = -2sin(x/2)(1/2)

dy/dx = -sin(x/2)

We now find d^2y/dx^2.

d^2y/dx^2 = -cos(x/2)(1/2)

d^2y/dx^2 = -(1/2)cos(x/2)

Answer 2

The value of 2nd derivative of y is,

$\dfrac{d^2y}{dx^2}= -\dfrac{1}{2} cos(\dfrac{x}{2})$

Given :

$y = 2cos(\dfrac{x}{2})$   ---- (1)

Solution :

Differentiate equation (1) with respect to x we get,

$\dfrac{dy}{dx}= -2sin(\dfrac{x}{2})\times \dfrac{1}{2}$

$\dfrac{dy}{dx}= -sin(\dfrac{x}{2})$   ----- (2)

Now differentiating equation (2) we get,

$\dfrac{d^2y}{dx^2}= -cos(\dfrac{x}{2})\times \dfrac{1}{2}$

$\dfrac{d^2y}{dx^2}= -\dfrac{1}{2} cos(\dfrac{x}{2})$

For more information, refer the link given below

https://brainly.com/question/14496325?referrer=searchResults