# Second Derivative of the Parametric Equation

__Parametric Function__

A function in which and are expressed as a function of a third variable is called a parametric function. For example, the function defined by the equations and is a parametric function.

Now we shall give an example to find the second derivative of the parametric function.

__Example__**:** If the parametric function , , then show that

We have the given parametric function

Differentiating both sides of equation (i) with respect to , we have

Differentiating both sides of equation (ii) with respect to , we have

Using the chain rule of differentiation , we have

Putting the values of and in the above chain rule formula, we have

Again, differentiating both sides with respect to , we have

Using the values of , we get

Putting the value of in the above result, we have