 Hi and welcome to the session. Today we will learn about derivatives of functions in parametric form. First of all let us learn what is parametric form. A relation expressed between two variables x and y in the form is equal to f of t and y is equal to t of t is said to be the parametric form and t is the parameter. Now suppose we want to find dy by dx then this will be equal to dy by dt that is differentiation of y with respect to t upon dx by dt that is differentiation of x with respect to t. Let us see one example for this. Here we are given x is equal to 5t and y is equal to 6 upon t and we need to find the value of dy by dx. Now we already know that dy by dx is equal to dy by dt upon dx by dt. Now x is equal to 5t so dx by dt is equal to 5 and y is equal to 6 upon t so dy by dt will be equal to 6 into minus 1 upon t square that is minus 6 upon t square. So dy by dx is equal to minus 6 upon t square upon 5 which is equal to minus 6 upon 5t square. Now let us move on to our next topic that is second order derivative. Suppose we are given y is equal to f of x then we will differentiate it with respect to x and we will get dy by dx is equal to f dash of x and now if f dash of x is differentiable then we can differentiate this equation again with respect to x. So we get dy by dx is equal to f double dash of x and this is denoted by d square y by dx square or d square of y that is second order derivative of y or y double dash or y2. So let us take one example to understand this. Here we are given y is equal to x cube plus 2x square minus 5 and we need to find second order derivative of y that is y double dash. So here my dash will be equal to 3x square plus 4x. So now differentiating again with respect to x we get y double dash is equal to 6x plus this session we have learnt derivatives of functions in parametric form and second order derivative. With this we finish this session and hope you must have understood all the concepts. Goodbye, take care and have a nice day.