# Second and higher derivatives.

Think of a function y=f(x) , and let y=f(x) be a differentiable function.

Then you can differentiate the function f(x) with respect to x or find derivative of f(x)= which is called the first derivative of the function f(x). Let the first derivative of the function be “y” and now if you again differentiate y with respect to “x” then the result is called **second derivative** of function f(x) you can again find it’s derivative and that’s called the **third derivative** of function f(x) and similarly you can differentiate again to find fourth , fifth , sixth…… derivative.

Mathematically you can denote second derivative as:

The third derivative is denoted by:

And you can also denote fourth , fifth and all higher derivative by changing the power of “d” and “x” to the respective number.

You can find the second , third , fourth and higher derivative using the following formula:

And so on…….

**Example of Second and Higher Derivative:**

Let us find the second , third , fourth and higher derivatives of the function:

f(x)=5x^{4}+4x^{3}-18

Solution:

The first derivative of the function=

The Second derivative of the function=

The third derivative of the function=

The fourth derivative of the function=

The fifth derivative of the function=

And as fifth derivative of the function f(x) is 0 sixth , seventh , eighth…. and all the higher derivative of the function will be 0.

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