2.2.57 Derivatives and differentials
Condition: Find the first \( d y / d x \) and second \( \left(d^{2} y\right) /\left(d x^{2}\right) \) derivatives of the function specified parametrically: \[ \left\{\begin{array}{l} x=1-t^{2} \\ y=t^{4}-8 t \end{array}\right. \]
Calculation of derivatives and differentials of first and higher orders of functions of one and many variables, including partial derivatives.