2.2.86 Derivatives and differentials
Condition: Calculate the value of the derivative of a complex function \( u=u(x, y) \), where \( x=x(t), y=y(t) \), with \( t=t_{0} \) accurate to two decimal places. \[ u=x^{y}, \quad x=e^{t}, \quad y=\ln t, \quad t_{0}=1 \]
Calculation of derivatives and differentials of first and higher orders of functions of one and many variables, including partial derivatives.