# Higher Order Derivatives

In this tutorial we shall find the higher order derivatives. We have already seen how differentiation is applied to a suitable function $f\left( x \right)$ and results in another function $f'\left( x \right)$. If $f'\left( x \right)$ is itself differentiable, then a repetition of differentiation will result in another function that we shall denote by $f''\left( x \right)$ and will call the second derivative of $f\left( x \right)$ with respect to $x$.

Using the definition of the derivative, we have

Similarly, the third and the fourth derivatives are

The successive derivatives of the function $y = f\left( x \right)$ are denoted by

OR

OR