**When derivative of any function itself differentiable, with the further derivative . Any derivative beyond the first derivative can be referred to as a higher order derivative.**

If y = f(x) thenÂ , the derivative of y with respect to x, is itself, in general , a function of x and can be differentiated again. To fix up the idea, we shall callÂ Â w.r.t. x as the first order derivative of y with respect to x and

the derivative ofÂ w.r.t. as the second order derivative of y w.r.t. x and will be denoted byÂ .

Similarly the derivative ofÂ w.r.t. x will be termed as the third order derivative of y w.r.t. x and will be denoted byÂ

and so on. the n^{th} order derivative of y w.r.t. x will be denoted byÂ

If y=f(x), then the other alternative notations for

The values of these derivatives at x=a are denoted by

### Example

**Solution:**

We haveÂ . On differentiating w.r.t. x , we get

Again differentiating w.r.t. x we get