log_likelihood := ( theta, s ) -> s * log( theta ) + 
  ( n - s ) * log( 1 - theta );

log_likelihood( theta, s );

# s * ln( theta ) + ( n - s ) * ln( 1 - theta )

diff( log_likelihood( theta, s ), theta );

# s / theta - ( n - s ) / ( 1 - theta )

simplify( diff( log_likelihood( theta, s ), theta ) );

# ( n * theta - s ) / ( theta * ( - 1 + theta ) )

solve( diff( log_likelihood( theta, s ), theta ) = 0, theta );

# s / n                         this is the MLE theta_hat of theta

simplify( - diff( log_likelihood( theta, s ), theta$2 ) );

# ( n * theta^2 - 2 * s * theta + s ) / ( theta^2 * ( -1 + theta )^2 )

simplify( eval( - diff( log_likelihood( theta, s ), theta$2 ), 
  theta = s / n ) );

# n^3 / ( ( n - s ) * s )       this is the Fisher information

simplify( eval( 1 / sqrt( - diff( log_likelihood( theta, s ), 
  theta$2 ) ), theta = s / n ) );

# 1 / sqrt( n^3 / ( ( n - s ) * s ) )    this is SE_hat( theta_hat )