 Hi and welcome to the session I am Shashi and I am going to help you with the following question. Question is if e raised to the power y multiplied by x plus 1 is equal to 1, show that d square y upon dx square is equal to dy upon dx square, let us start the solution now, we are given e raised to the power y multiplied by x plus 1 is equal to 1, this implies e raised to the power y is equal to 1 upon x plus 1, now differentiating both sides with respect to x we get, we will get e raised to the power y dy upon dx, we know derivative of e raised to the power y is e raised to the power y multiplied by dy by dx, we will apply the chain rule here, first we have found the derivative of e raised to the power y and then the derivative of y, now this is further equal to here we will apply the question rule, so we can write x plus 1 multiplied by derivative of 1 minus 1 multiplied by derivative of x plus 1 upon x plus 1 whole square, so this is further equal to e raised to the power y dy by dx is equal to 0 minus 1, here the derivative of x plus 1 would be equal to 1, so 1 multiplied by minus 1 is equal to minus 1, so we get minus 1 upon x plus 1 whole square or we can say e raised to the power y dy upon dx is equal to minus 1 upon x plus 1 whole square, now we know e raised to the power y is equal to 1 upon x plus 1, let us name this expression as 1, now substituting this value of e raised to the power y in this expression we get 1 upon x plus 1 multiplied by dy upon dx is equal to minus 1 upon x plus 1 whole square, now this implies dy upon dx is equal to minus 1 upon x plus 1, now again differentiating both sides with respect to x we get d square y upon dx square is equal to x plus 1 multiplied by derivative of minus 1 minus minus 1 multiplied by derivative of x plus 1 upon x plus 1 whole square, here we have applied cohesion rule, now this implies d square y upon dx square is equal to minus minus 1 upon x plus 1 whole square or we can say d square y upon dx square is equal to minus 1 upon x plus 1 whole square, we know minus 1 upon x plus 1 is equal to dy upon dx, let us name this expression as 2, now we can write this implies d square y upon dx square is equal to dy upon dx square, so this is our required answer, so we can write d square y upon dx square is equal to dy upon dx whole square, hence proved this completes the session, hope you understood the session take care and goodbye.