# List of Notes - Category: Higher-Order Derivatives

## Definition of Higher-Order Derivatives

If f(x) is a differentiable function, then its derivative f'(x) is also a function, so may have a derivative (finite or not). This function is called second derivative of f(x) because it is derivative of derivative and denoted by f'' . So, f''=(f')'.

## Formulas for Higher-Order Derivatives

In general, to find n-th derivative of function y=f(x) we need to find all derivatives of previous orders. But sometimes it is possible to obtain expression for n-th derivative that depends on n and doesn't contain previous derivatives.

## Higher-Order Differentials

Differential of the second order of function y=f(x) is differential of first differential of the function: d^2y=d(dy).

Differential of the third order of function y=f(x) is differential of second differential of the function: d^3y=d(d^2y).

## Parametric Differentiating

Sometimes we need to write derivatives with respect to x through differentials of another variable t. In this case expression for derivatives will be more complex.

So, let's calculate differentials with respect to t, in other words x is not an independent variable.