def diff(y, x):
    """Return the symbolic derivative, dy/dx, as an Expr.
    However, you probably want to simplify the results with simp.
    >>> diff(x * x, x)
    ((x * 1) + (x * 1))
    >>> simp(diff(x * x, x))
    (2 * x)
    """
    if y == x: return ONE
    elif not y.args: return ZERO
    else:
        u, op, v = y.args[0], y.op, y.args[-1]
        if op == '+': return diff(u, x) + diff(v, x)
        elif op == '-' and len(args) == 1: return -diff(u, x)
        elif op == '-': return diff(u, x) - diff(v, x)
        elif op == '*': return u * diff(v, x) + v * diff(u, x)
        elif op == '/': return (v*diff(u, x) - u*diff(v, x)) / (v * v)
        elif op == '**' and isnumber(x.op):
            return (v * u ** (v - 1) * diff(u, x))
        elif op == '**': return (v * u ** (v - 1) * diff(u, x)
                                 + u ** v * Expr('log')(u) * diff(v, x))
        elif op == 'log': return diff(u, x) / u
        else: raise ValueError("Unknown op: %s in diff(%s, %s)" % (op, y, x))
def diff(y, x):
    """Return the symbolic derivative, dy/dx, as an Expr.
    However, you probably want to simplify the results with simp.
    >>> diff(x * x, x)
    ((x * 1) + (x * 1))
    >>> simp(diff(x * x, x))
    (2 * x)
    """
    if y == x: return ONE
    elif not y.args: return ZERO
    else:
        u, op, v = y.args[0], y.op, y.args[-1]
        if op == '+': return diff(u, x) + diff(v, x)
        elif op == '-' and len(args) == 1: return -diff(u, x)
        elif op == '-': return diff(u, x) - diff(v, x)
        elif op == '*': return u * diff(v, x) + v * diff(u, x)
        elif op == '/': return (v*diff(u, x) - u*diff(v, x)) / (v * v)
        elif op == '**' and isnumber(x.op):
            return (v * u ** (v - 1) * diff(u, x))
        elif op == '**': return (v * u ** (v - 1) * diff(u, x)
                                 + u ** v * Expr('log')(u) * diff(v, x))
        elif op == 'log': return diff(u, x) / u
        else: raise ValueError("Unknown op: %s in diff(%s, %s)" % (op, y, x))
def diff ( y , x ) : if y == x : return ONE elif not y . args : return ZERO else : u , op , v = y . args [ 0 ] , y . op , y . args [ - 1 ] if op == '+' : return diff ( u , x ) + diff ( v , x ) elif op == '-' and len ( args ) == 1 : return - diff ( u , x ) elif op == '-' : return diff ( u , x ) - diff ( v , x ) elif op == '*' : return u * diff ( v , x ) + v * diff ( u , x ) elif op == '/' : return ( v * diff ( u , x ) - u * diff ( v , x ) ) / ( v * v ) elif op == '**' and isnumber ( x . op ) : return ( v * u ** ( v - 1 ) * diff ( u , x ) ) elif op == '**' : return ( v * u ** ( v - 1 ) * diff ( u , x ) + u ** v * Expr ( 'log' ) ( u ) * diff ( v , x ) ) elif op == 'log' : return diff ( u , x ) / u else : raise ValueError ( "Unknown op: %s in diff(%s, %s)" % ( op , y , x ) )
Return the symbolic derivative, dy/dx, as an Expr.
    However, you probably want to simplify the results with simp.
    >>> diff(x * x, x)
    ((x * 1) + (x * 1))
    >>> simp(diff(x * x, x))
    (2 * x)
Return the symbolic derivative dy / dx as an Expr . However you probably want to simplify the results with simp . >>> diff ( x * x x ) (( x * 1 ) + ( x * 1 )) >>> simp ( diff ( x * x x )) ( 2 * x )