MathProblemsBank

2.2.9 Derivatives and differentials

Problem: A complex function is given: \[ z=\frac{y}{x} \text {, where } x=e^{t}, y=1-e^{2 t} \text {. } \] Find \( \frac{d z}{d t}, \quad \frac{d^{2} z}{d t^{2}} \).