diff --git a/sumpy/tools.py b/sumpy/tools.py
index bec9ea9ba14e1a4a5b7d59c0be57d1ea501bfa68..89192f78b0af71fb03adef00014a96918b3b1a89 100644
--- a/sumpy/tools.py
+++ b/sumpy/tools.py
@@ -46,6 +46,7 @@ import numpy as np
 import sumpy.symbolic as sym
 
 import loopy as lp
+from typing import Dict, Tuple, Any
 
 import logging
 logger = logging.getLogger(__name__)
@@ -394,6 +395,9 @@ class HelmholtzDerivativeTaker(RadialDerivativeTaker):
         return expr
 
 
+DerivativeCoeffDict = Dict[Tuple[int], Any]
+
+
 @tag_dataclass
 class DifferentiatedExprDerivativeTaker:
     """Implements the :class:`ExprDerivativeTaker` interface
@@ -411,7 +415,7 @@ class DifferentiatedExprDerivativeTaker:
         base expression.
     """
     taker: ExprDerivativeTaker
-    derivative_coeff_dict: dict
+    derivative_coeff_dict: DerivativeCoeffDict
 
     def diff(self, mi, save_intermediate=lambda x: x):
         # By passing `rscale` to the derivative taker we are taking a scaled
@@ -432,7 +436,8 @@ class DifferentiatedExprDerivativeTaker:
         return result * save_intermediate(1 / self.taker.rscale ** max_order)
 
 
-def diff_derivative_coeff_dict(derivative_coeff_dict, variable_idx, variables):
+def diff_derivative_coeff_dict(derivative_coeff_dict: DerivativeCoeffDict,
+        variable_idx, variables):
     """Differentiate a derivative transformation dictionary given by
     *derivative_coeff_dict* using the variable given by **variable_idx**
     and return a new derivative transformation dictionary.