Differentiating polynomials for pros
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Exercise:
nprvmulticols abclist abc displaystyle fracddddx left alpha x^n right abc displaystyle fracddddy left beta y^m + gamma y^n right abc displaystyle fracddddz left lambda z^a z^b + mu right abc displaystyle fracddddtheta left delta theta^k + varepsilon^n right abc displaystyle fracddddphi left phi^n + alphaphi^m + beta right abc displaystyle fracddddw left w^p gamma + rho w^r^q right abc displaystyle fracddddxi left xi^m + nu^n xi^n + zeta^m right abc displaystyle fracdddda left kappa + lambda a^s^sigma right abc displaystyle fracddddb left b^n b^m + alpha^eta right abc displaystyle fracddddchi left chi^k + omega chi^n^r right abc displaystyle fracddddr left beta + gamma r^u^rho delta + epsilon r^v^sigma right abc displaystyle fracddddpsi left psi^lambda psi^mu + theta^xi right abclist nprvmulticols
Solution:
Solutions: abclist abc displaystyle fracddddx left alpha x^n right alpha n x^n - abc displaystyle fracddddy left beta y^m + gamma y^n right beta m y^m - + gamma n y^n - abc displaystyle fracddddz left lambda z^a z^b + mu right lambda a z^a - z^b + mu + lambda z^a b z^b - abc displaystyle fracddddtheta left delta theta^k + varepsilon^n right n delta theta^k + varepsilon^n - delta k theta^k - abc displaystyle fracddddphi left phi^n + alphaphi^m + beta right n phi^n - phi^m + beta + m phi^m - phi^n + alpha abc displaystyle fracddddw left w^p gamma + rho w^r^q right p w^p - gamma + rho w^r^q + w^p qgamma + rho w^r^q - rho r w^r - abc displaystyle fracddddxi left xi^m + nu^n xi^n + zeta^m right nxi^m + nu^n - m xi^m - xi^n + zeta^m + mxi^n + zeta^m - n xi^n - xi^m + nu^n abc displaystyle fracdddda left kappa + lambda a^s^sigma right sigma kappa + lambda a^s^sigma - lambda s a^s - abc displaystyle fracddddb left b^n b^m + alpha^eta right n b^n - b^m + alpha^eta + b^n etab^m + alpha^eta - m b^m - abc displaystyle fracddddchi left chi^k + omega chi^n^r right rchi^k + omega chi^n^r - k chi^k - + omega n chi^n - abc displaystyle fracddddr left beta + gamma r^u^rho delta + epsilon r^v^sigma right rho beta + gamma r^u^rho - gamma u r^u - delta + epsilon r^v^sigma + sigma delta + epsilon r^v^sigma - epsilon v r^v - beta + gamma r^u^rho abc displaystyle fracddddpsi left psi^lambda psi^mu + theta^xi right lambda psi^lambda - psi^mu + theta^xi + psi^lambda xi psi^mu + theta^xi - mu psi^mu - abclist
nprvmulticols abclist abc displaystyle fracddddx left alpha x^n right abc displaystyle fracddddy left beta y^m + gamma y^n right abc displaystyle fracddddz left lambda z^a z^b + mu right abc displaystyle fracddddtheta left delta theta^k + varepsilon^n right abc displaystyle fracddddphi left phi^n + alphaphi^m + beta right abc displaystyle fracddddw left w^p gamma + rho w^r^q right abc displaystyle fracddddxi left xi^m + nu^n xi^n + zeta^m right abc displaystyle fracdddda left kappa + lambda a^s^sigma right abc displaystyle fracddddb left b^n b^m + alpha^eta right abc displaystyle fracddddchi left chi^k + omega chi^n^r right abc displaystyle fracddddr left beta + gamma r^u^rho delta + epsilon r^v^sigma right abc displaystyle fracddddpsi left psi^lambda psi^mu + theta^xi right abclist nprvmulticols
Solution:
Solutions: abclist abc displaystyle fracddddx left alpha x^n right alpha n x^n - abc displaystyle fracddddy left beta y^m + gamma y^n right beta m y^m - + gamma n y^n - abc displaystyle fracddddz left lambda z^a z^b + mu right lambda a z^a - z^b + mu + lambda z^a b z^b - abc displaystyle fracddddtheta left delta theta^k + varepsilon^n right n delta theta^k + varepsilon^n - delta k theta^k - abc displaystyle fracddddphi left phi^n + alphaphi^m + beta right n phi^n - phi^m + beta + m phi^m - phi^n + alpha abc displaystyle fracddddw left w^p gamma + rho w^r^q right p w^p - gamma + rho w^r^q + w^p qgamma + rho w^r^q - rho r w^r - abc displaystyle fracddddxi left xi^m + nu^n xi^n + zeta^m right nxi^m + nu^n - m xi^m - xi^n + zeta^m + mxi^n + zeta^m - n xi^n - xi^m + nu^n abc displaystyle fracdddda left kappa + lambda a^s^sigma right sigma kappa + lambda a^s^sigma - lambda s a^s - abc displaystyle fracddddb left b^n b^m + alpha^eta right n b^n - b^m + alpha^eta + b^n etab^m + alpha^eta - m b^m - abc displaystyle fracddddchi left chi^k + omega chi^n^r right rchi^k + omega chi^n^r - k chi^k - + omega n chi^n - abc displaystyle fracddddr left beta + gamma r^u^rho delta + epsilon r^v^sigma right rho beta + gamma r^u^rho - gamma u r^u - delta + epsilon r^v^sigma + sigma delta + epsilon r^v^sigma - epsilon v r^v - beta + gamma r^u^rho abc displaystyle fracddddpsi left psi^lambda psi^mu + theta^xi right lambda psi^lambda - psi^mu + theta^xi + psi^lambda xi psi^mu + theta^xi - mu psi^mu - abclist