Find the second order derivatives of the functions given.
`sin(log x)`

Explanation

Let `y=sin(log x)`

Differentiating w.r.t. x

`dy/dx=(d(sin(logx)))/dx`

`dy/dx=cos(logx).(d(logx))/dx`

`dy/dx=cos(logx).(1)/(x)`

`dy/dx=cos(logx)/(x)`

Again Differentiating w.r.t. x

`d/dx(dy/dx)=d/dx(cos(logx)/(x))`

`(d^2y)/(dx^2)=d/dx(cos(logx)/(x))`

Using Quotient Rule

`(d^2y)/(dx^2)=((d(cos(logx)))/(dx).x-(d(x))/dx.cos(logx))/x^2`

`(d^2y)/(dx^2)=(-sin(logx).(d(logx))/(dx).x-1.cos(logx))/x^2`

`(d^2y)/(dx^2)=(-sin(logx).(1)/x.x-1.cos(logx))/x^2`

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

`(d^2y)/(dx^2)=(-[sin(logx)+cos(logx)])/x^2`