The derivative of a function is also a function. If f(x) is differentiable then f'(x) is also a function of x. If f'(x) is also differentiable, then we can find its derivative function as well which is denoted by f"(x). Thus the process of differentiation can be continued successively as long as each derivative in the sequence is differentiable. The higher order derivatives so found by repeated differentiation play an important role in the study and application of Calculus

The second derivative is the derivative function of the first derivative and it is denoted by f"(x). Second derivative is used determining the Extreme values of the functions and its concavity.
In general, the second derivative can be interpreted as the rate of change of rate of change. If s (t) the position of a moving particle a function of t, then the velocity v(t) is given by the first derivative s'(t) and the acceleration a(t) by the second derivative s"(t).

## Second Derivative Definition

The second derivative of an at least twice differentiable function is the function got by differentiating the given function twice in succession.

If f is a differentiable function and if its derivative f' is also differentiable, then the second derivative f" = f=(f')'.

The prime notation used to indicate the second derivative of y = f(x) is either y" or f "(x).

Leibniz notation for the same is $\frac{d^{2}y}{dx^{2}}$

Other alternate notations are D2 f(x) or D2 y.
Using Leibniz notation the definition of second derivative can be shown as
$\frac{d^{2}y}{dx^{2}}$ = $\frac{d}{dx}(\frac{dy}{dx})$

### Partial Derivative

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