Final answer:
To find ²y/dx² when x=e²ᵗ and y=sin(2t), we must apply the chain rule and differentiate implicitly; however, the calculation requires a specific relationship between x and y.
Step-by-step explanation:
The student has presented a calculus problem involving finding the second derivative of y with respect to x, where x and y are functions of the variable t. Since x and y are given by x=e²ᵗ and y=sin(2t), respectively, we first need to find dy/dx and then d²y/dx². This involves applying the chain rule, as well as differentiating implicitly because y is given in terms of t. However, without a clear relationship between x and y to differentiate, we cannot directly calculate d²y/dx², but instead, we can describe the process of how one would approach such a problem if the interdependent relationship between x and y was apparent.