2.2.89 Derivatives and differentials
condition: Check whether the given function \(u\) satisfies the specified equation. \[ a^{2} \frac{\partial^{2} u}{\partial x^{2}}=\frac{\partial^{2} u}{\partial y^{2}}, \quad u=\sin ^{2}(x-a y)\]
Calculation of derivatives and differentials of first and higher orders of functions of one and many variables, including partial derivatives.