Differentiation

If \(x^{\mathrm{k}}+y^{\mathrm{k}}=\mathrm{a}^{\mathrm{k}}(\mathrm{a}, \mathrm{k}>0)\) and \(\frac{\mathrm{d} y}{\mathrm{~d} x}+\left(\frac{y}{x}\right)^{\frac{1}{3}}=0\), then \(\mathrm{k}\) has the value