diff --git a/docs/source/numerical_derivatives.rst b/docs/source/numerical_derivatives.rst
index 57b46bf..8d7fb3a 100644
--- a/docs/source/numerical_derivatives.rst
+++ b/docs/source/numerical_derivatives.rst
@@ -61,8 +61,7 @@
   }
 
   CostFunction* cost_function =
-    new NumericDiffCostFunction<Rat43CostFunctor, FORWARD, 1, 4>(
-      new Rat43CostFunctor(x, y));
+    new NumericDiffCostFunction<Rat43CostFunctor, FORWARD, 1, 4>(x, y);
 
 This is about the minimum amount of work one can expect to do to
 define the cost function. The only thing that the user needs to do is
@@ -326,7 +325,7 @@
 Compared to the *correct* value :math:`Df(1.0) = 140.73773557129658`,
 :math:`A(5, 1)` has a relative error of :math:`10^{-13}`. For
 comparison, the relative error for the central difference formula with
-the same stepsize (:math:`0.01/2^4 = 0.000625`) is :math:`10^{-5}`.
+the same step size (:math:`0.01/2^4 = 0.000625`) is :math:`10^{-5}`.
 
 The above tableau is the basis of Ridders' method for numeric
 differentiation. The full implementation is an adaptive scheme that