diff --git a/sumpy/kernel.py b/sumpy/kernel.py
index efb4b09398f40bb0ad87e54bebc250ae877b254c..d88ec3d6a44088646a73192227ab4a523095c0e7 100644
--- a/sumpy/kernel.py
+++ b/sumpy/kernel.py
@@ -222,7 +222,7 @@ class Kernel:
         from sumpy.tools import (ExprDerivativeTaker,
             DifferentiatedExprDerivativeTaker)
         expr_dict = {(0,)*self.dim: 1}
-        expr_dict = self.get_derivative_transformation_at_source(expr_dict)
+        expr_dict = self.get_derivative_coeff_dict_at_source(expr_dict)
         if isinstance(expr, ExprDerivativeTaker):
             return DifferentiatedExprDerivativeTaker(expr, expr_dict)
 
@@ -244,7 +244,7 @@ class Kernel:
         """
         return expr
 
-    def get_derivative_transformation_at_source(self, expr_dict):
+    def get_derivative_coeff_dict_at_source(self, expr_dict):
         r"""Get the derivative transformation of the expression at source
         represented by the dictionary expr_dict which is mapping from multi-index
         `mi` to coefficient `coeff`.
@@ -939,8 +939,8 @@ class KernelWrapper(Kernel):
     def get_expression(self, scaled_dist_vec):
         return self.inner_kernel.get_expression(scaled_dist_vec)
 
-    def get_derivative_transformation_at_source(self, expr_dict):
-        return self.inner_kernel.get_derivative_transformation_at_source(expr_dict)
+    def get_derivative_coeff_dict_at_source(self, expr_dict):
+        return self.inner_kernel.get_derivative_coeff_dict_at_source(expr_dict)
 
     def postprocess_at_target(self, expr, bvec):
         return self.inner_kernel.postprocess_at_target(expr, bvec)
@@ -989,8 +989,8 @@ class AxisSourceDerivative(DerivativeBase):
     def __repr__(self):
         return "AxisSourceDerivative(%d, %r)" % (self.axis, self.inner_kernel)
 
-    def get_derivative_transformation_at_source(self, expr_dict):
-        expr_dict = self.inner_kernel.get_derivative_transformation_at_source(
+    def get_derivative_coeff_dict_at_source(self, expr_dict):
+        expr_dict = self.inner_kernel.get_derivative_coeff_dict_at_source(
             expr_dict)
         result = dict()
         for mi, coeff in expr_dict.items():
@@ -1028,7 +1028,7 @@ class AxisTargetDerivative(DerivativeBase):
 
     def postprocess_at_target(self, expr, bvec):
         from sumpy.tools import (DifferentiatedExprDerivativeTaker,
-                diff_transformation)
+                diff_derivative_coeff_dict)
         from sumpy.symbolic import make_sym_vector as make_sympy_vector
 
         target_vec = make_sympy_vector(self.target_array_name, self.dim)
@@ -1036,7 +1036,7 @@ class AxisTargetDerivative(DerivativeBase):
         # bvec = tgt - ctr
         expr = self.inner_kernel.postprocess_at_target(expr, bvec)
         if isinstance(expr, DifferentiatedExprDerivativeTaker):
-            transformation = diff_transformation(expr.derivative_transformation,
+            transformation = diff_derivative_coeff_dict(expr.derivative_coeff_dict,
                     self.axis, target_vec)
             return DifferentiatedExprDerivativeTaker(expr.taker, transformation)
         else:
@@ -1123,7 +1123,7 @@ class DirectionalTargetDerivative(DirectionalDerivative):
 
     def postprocess_at_target(self, expr, bvec):
         from sumpy.tools import (DifferentiatedExprDerivativeTaker,
-                diff_transformation)
+                diff_derivative_coeff_dict)
 
         from sumpy.symbolic import make_sym_vector as make_sympy_vector
         dir_vec = make_sympy_vector(self.dir_vec_name, self.dim)
@@ -1143,8 +1143,8 @@ class DirectionalTargetDerivative(DirectionalDerivative):
 
         new_transformation = defaultdict(lambda: 0)
         for axis in range(self.dim):
-            axis_transformation = diff_transformation(
-                    expr.derivative_transformation, axis, target_vec)
+            axis_transformation = diff_derivative_coeff_dict(
+                    expr.derivative_coeff_dict, axis, target_vec)
             for mi, coeff in axis_transformation.items():
                 new_transformation[mi] += coeff * dir_vec[axis]
 
@@ -1180,11 +1180,11 @@ class DirectionalSourceDerivative(DirectionalDerivative):
 
         return transform
 
-    def get_derivative_transformation_at_source(self, expr_dict):
+    def get_derivative_coeff_dict_at_source(self, expr_dict):
         from sumpy.symbolic import make_sym_vector as make_sympy_vector
         dir_vec = make_sympy_vector(self.dir_vec_name, self.dim)
 
-        expr_dict = self.inner_kernel.get_derivative_transformation_at_source(
+        expr_dict = self.inner_kernel.get_derivative_coeff_dict_at_source(
             expr_dict)
 
         # avec = center-src -> minus sign from chain rule
@@ -1251,7 +1251,7 @@ class TargetPointMultiplier(KernelWrapper):
 
         if isinstance(expr, DifferentiatedExprDerivativeTaker):
             transform = {mi: coeff * mult for mi, coeff in
-                    expr.derivative_transformation.items()}
+                    expr.derivative_coeff_dict.items()}
             return DifferentiatedExprDerivativeTaker(expr.taker, transform)
         elif isinstance(expr, ExprDerivativeTaker):
             return DifferentiatedExprDerivativeTaker({zeros: mult})
diff --git a/sumpy/tools.py b/sumpy/tools.py
index 0638aca1611e689828f4a602e26d9515bc3b18d7..bec9ea9ba14e1a4a5b7d59c0be57d1ea501bfa68 100644
--- a/sumpy/tools.py
+++ b/sumpy/tools.py
@@ -404,41 +404,41 @@ class DifferentiatedExprDerivativeTaker:
     .. attribute:: taker
         A :class:`ExprDerivativeTaker` for the base expression.
 
-    .. attribute:: derivative_transformation
+    .. attribute:: derivative_coeff_dict
         A dictionary mapping a derivative multi-index to a coefficient.
         The expression represented by this derivative taker is the linear
         combination of the derivatives of the expression for the
         base expression.
     """
     taker: ExprDerivativeTaker
-    derivative_transformation: dict
+    derivative_coeff_dict: dict
 
     def diff(self, mi, save_intermediate=lambda x: x):
         # By passing `rscale` to the derivative taker we are taking a scaled
         # version of the derivative which is `expr.diff(mi)*rscale**sum(mi)`
         # which might be implemented efficiently for kernels like Laplace.
         # One caveat is that we are taking more derivatives because of
-        # :attr:`derivative_transformation` which would multiply the
+        # :attr:`derivative_coeff_dict` which would multiply the
         # expression by more `rscale`s than necessary. This is corrected by
         # dividing by `rscale`.
         max_order = max(sum(extra_mi) for extra_mi in
-                self.derivative_transformation.keys())
+                self.derivative_coeff_dict.keys())
 
         result = sum(
             coeff * self.taker.diff(add_mi(mi, extra_mi))
             / self.taker.rscale ** (sum(extra_mi) - max_order)
-            for extra_mi, coeff in self.derivative_transformation.items())
+            for extra_mi, coeff in self.derivative_coeff_dict.items())
 
         return result * save_intermediate(1 / self.taker.rscale ** max_order)
 
 
-def diff_transformation(derivative_transformation, variable_idx, variables):
-    """Differentiate a derivative transformation dictionary using the
-    variable given by **variable_idx** and return a new derivative transformation
-    dictionary
+def diff_derivative_coeff_dict(derivative_coeff_dict, 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.
     """
     new_derivative_coeff_dict = defaultdict(lambda: 0)
-    for mi, coeff in derivative_transformation.items():
+    for mi, coeff in derivative_coeff_dict.items():
         # In the case where we have x * u.diff(x), the result should
         # be x.diff(x) + x * u.diff(x, x)
         # Calculate the first term by differentiating the coefficients