# Second Derivative of Parametric Equation

__Parametric Function__**:**

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

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

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

We have 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 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

Putting the values of , we get

Putting the value of in the above result, we have