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