 Hi and welcome to the session. I am Priyanka and let us discuss the following question. It says, find d y by g x if x and y are connected parametrically by the equations without animating the parameter. Now here we are given equal to 2 a t square and y equal to a t raised to the power 4. Now in such case x and y are called parametric function and t is called the parameter. Here we can find d y by d x by following a formula that says d y divided by d t the whole divided by d x divided by d t. So the knowledge of this formula is the key idea that we are going to use in order to proceed on with our solution. According to this formula we know that first of all we need to differentiate y with respect to t and then x with respect to t and then divide the answers to get dy by d x right. Now here x is equal to 2 a t square and y is equal to a t raised to the power 4. Now first of all we will be finding out dx by dt that is we will be finding out the derivative with respect to t that will be dy dt of 2 a t square whereas here we will find out dy by dt and dy dt of a t raised to the power 4. So we have dx by dt as 2 a multiplied by 2 t that is equal to 4 a t whereas dy by dt is equal to 4 a t raised to the power 3. Now what are we supposed to do as discussed in the formula above in order to find out dy by dt or dx we will be dividing dy by dt with dx by dt and then we have 4 a t cube divided by 4 a t 4 will get cancelled out a will get cancelled out and we have t raised to the power 3 minus 1 that is equal to t raised to the power 2. So dy by dt or dy by dx this is what we were finding out is equal to 2 raised x t raised to the power 2 right. So this is our required answer I hope you enjoyed the session take care