diff --git a/src/calculus.jl b/src/calculus.jl
index 60b542b..837188d 100644
--- a/src/calculus.jl
+++ b/src/calculus.jl
@@ -5,30 +5,64 @@ import Base: diff
 ## what is the rest of the interface. This does:
 ## diff(ex, x, n)      f^(n)
 ## diff(ex, x, y, ...) f_{xy...}  # also diff(ex, (x,y))
-## no support for diff(ex, x,n1, y,n2, ...), but can do diff(ex, (x,y), (n1, n2))
+## Support for diff(ex, x,n1, y,n2, ...),
+## but can also do diff(ex, (x,y), (n1, n2))
 
-function diff(b1::SymbolicType, b2::BasicType{Val{:Symbol}})
-    a = Basic()
+
+function diff!(a::Basic, b1::SymbolicType, b2::Basic)
+    is_symbol(b2) || throw(ArgumentError("Must differentiate with respect to a symbol"))
     ret = ccall((:basic_diff, libsymengine), Int, (Ref{Basic}, Ref{Basic}, Ref{Basic}), a, b1, b2)
     return a
 end
 
-diff(b1::SymbolicType, b2::BasicType) =
-    throw(ArgumentError("Second argument must be of Symbol type"))
+function diff(b1::SymbolicType, b2::Basic)
+    a = Basic()
+    diff!(a, b1, b2)
+    a
+end
 
-function diff(b1::SymbolicType, b2::SymbolicType, n::Integer=1)
+function diff(b1::SymbolicType, b2::SymbolicType, n::Integer)
     n < 0 && throw(DomainError("n must be non-negative integer"))
-    n==0 && return b1
-    n==1 && return diff(b1, BasicType(b2))
-    n > 1 && return diff(diff(b1, BasicType(b2)), BasicType(b2), n-1)
+    n == 0 && return b1
+    x = Basic(b2)
+    out = Basic()
+    diff!(out, b1, x)
+    for _ in (n-1):-1:1
+        diff!(out, out, x)
+    end
+    out
+end
+
+function diff(b1::SymbolicType, b2::SymbolicType, n::Integer, xs...)
+    diff(diff(b1,b2,n), xs...)
 end
 
 function diff(b1::SymbolicType, b2::SymbolicType, b3::SymbolicType)
-    isa(BasicType(b3), BasicType{Val{:Integer}}) ? diff(b1, b2, N(b3)) : diff(b1, (b2, b3))
+    if isinteger(b3)
+        n = N(b3)::Int
+        diff(b1, b2, n)
+    else
+        ex = diff(b1, b2)
+        diff(ex, b3)
+    end
+end
+
+function diff(b1::SymbolicType, b2::SymbolicType, b3::SymbolicType, bs...)
+    diff(diff(b1,b2,b3), bs...)
 end
 
-diff(b1::SymbolicType, b2::SymbolicType, b3::SymbolicType, b4::SymbolicType, b5...) =
-    diff(b1, (b2,b3,b4,b5...))
+function diff(b1::SymbolicType)
+    xs = free_symbols(b1)
+    n = length(xs)
+    n == 0 && return zero(b1)
+    n > 1 && throw(ArgumentError("More than one variable; one must be specified"))
+    diff(b1, only(xs))
+end
+
+## deprecate
+diff(b1::SymbolicType, b2::BasicType{Val{:Symbol}}) = diff(b1, Basic(b2))
+diff(b1::SymbolicType, b2::BasicType) =
+    throw(ArgumentError("Second argument must be of Symbol type"))
 
 ## mixed partials
 diff(ex::SymbolicType, bs::Tuple) = reduce((ex, x) -> diff(ex, x), bs, init=ex)
diff --git a/test/runtests.jl b/test/runtests.jl
index a3ba7b8..01c0f52 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -101,14 +101,22 @@ u,v,w = x(2.1), x(1), x(0)
 
 ## calculus
 x,y = symbols("x y")
+@test diff(log(x)) == 1/x
+@test diff(log(x),x) == 1/x
+@test_throws ArgumentError diff(log(x), x^2)
+
 n = Basic(2)
 ex = sin(x*y)
-@test diff(log(x),x) == 1/x
+@test_throws ArgumentError diff(ex)
 @test diff(ex, x) == y * cos(x*y)
 @test diff(ex, x, 2) == diff(diff(ex,x), x)
 @test diff(ex, x, n) == diff(diff(ex,x), x)
 @test diff(ex, x, y) == diff(diff(ex,x), y)
-@test diff(ex, x, y,x) == diff(diff(diff(ex,x), y), x)
+@test diff(ex, x, y, x) == diff(diff(diff(ex,x), y), x)
+@test diff(ex, x, 2, y, 3) == diff(ex, x,x,y,y,y)
+@test diff(ex, x, n, y, 3) == diff(ex, x,x,y,y,y)
+@test diff(ex, x, 2, y, x) == diff(ex, x,x,x,y)
+
 @test series(sin(x), x, 0, 2) == x
 @test series(sin(x), x, 0, 3) == x - x^3/6