Wronskian dari $$$x$$$, $$$\frac{1}{x^{5}}$$$

Hitung Wronskian dari $$$\left\{f_{1} = x, f_{2} = \frac{1}{x^{5}}\right\}$$$.

Wronskian diberikan oleh determinan berikut: $$$W{\left(f_{1},f_{2} \right)}\left(x\right) = \left|\begin{array}{cc}f_{1}\left(x\right) & f_{2}\left(x\right)\\f_{1}^{\prime}\left(x\right) & f_{2}^{\prime}\left(x\right)\end{array}\right|.$$$

Dalam kasus ini, $$$W{\left(f_{1},f_{2} \right)}\left(x\right) = \left|\begin{array}{cc}x & \frac{1}{x^{5}}\\\left(x\right)^{\prime } & \left(\frac{1}{x^{5}}\right)^{\prime }\end{array}\right|.$$$

Temukan turunan (untuk langkah-langkahnya, lihat kalkulator turunan): $$$W{\left(f_{1},f_{2} \right)}\left(x\right) = \left|\begin{array}{cc}x & \frac{1}{x^{5}}\\1 & - \frac{5}{x^{6}}\end{array}\right|$$$

Temukan determinan (untuk langkah-langkah, lihat kalkulator determinan): $$$\left|\begin{array}{cc}x & \frac{1}{x^{5}}\\1 & - \frac{5}{x^{6}}\end{array}\right| = - \frac{6}{x^{5}}$$$

Wronskian sama dengan $$$- \frac{6}{x^{5}}$$$A.