Question

How do you find the second derivative of `y=2sin3x-5sin6x`?

Answer 1

First find the first derivative using the chain rule.

`dy/dx=6cos(3x)-30cos(6x)`

Now take the derivative again to find the second derivative

`(d^2y)/dx^2=-18sin(3x)+180sin(6x)`

Answer 2

Hello,

Answer `y'' = -18 sin(3x) + 180 sin(6x)`.

• First, you calculate the derivative :
  `y' = 2 cos(3x)\times 3 - 5 cos(6x)\times 6`.

I used `d/dx sin(nx) = cos(nx)\times n`.

• You can simplify :
  `y' = 6 cos(3x) - 30 cos(6x)`.

• Now, you calculate the second derivative :
  `y'' = -6 sin(3x) \times 3 + 30 sin(6x)\times 6`

I used `d/dx cos(nx) = -sin(nx)\times n`.

You can also simplify to obtain the result.