diff --git a/extra_credit/README.md b/extra_credit/README.md
index 1e348f0..802e961 100644
--- a/extra_credit/README.md
+++ b/extra_credit/README.md
@@ -41,7 +41,7 @@ and gradient
 
 ![costgrad](./equations/costgrad.png)
 
-where ![x](./equations/x.png) is the k-th value of temperature raised to the i-th power (0, and 1)
+where ![x](./equations/x.png) is the i-th value of temperature raised to the k-th power (0, and 1)
 
 a. edit `cost_logistic.m` so that the output is `[J,grad]` or [cost, gradient]
 
diff --git a/extra_credit/equations/cost.png b/extra_credit/equations/cost.png
index c1092a7..f503c96 100644
Binary files a/extra_credit/equations/cost.png and b/extra_credit/equations/cost.png differ
diff --git a/extra_credit/equations/cost.tex b/extra_credit/equations/cost.tex
index 0a5d023..5f8aa2c 100644
--- a/extra_credit/equations/cost.tex
+++ b/extra_credit/equations/cost.tex
@@ -1,2 +1,2 @@
-J(a_{0},a_{1})=1/m\sum_{i=1}^{n}\left[-y_{i}\log(\sigma(t_{i}))-(1-y_{i})\log((1-\sigma(t_{i})))\right]
+J(a_{0},a_{1})=\sum_{i=1}^{n}\left[-y_{i}\log(\sigma(t_{i}))-(1-y_{i})\log((1-\sigma(t_{i})))\right]
 
diff --git a/extra_credit/equations/costgrad.png b/extra_credit/equations/costgrad.png
index 15eb272..aaa9fa9 100644
Binary files a/extra_credit/equations/costgrad.png and b/extra_credit/equations/costgrad.png differ
diff --git a/extra_credit/equations/costgrad.tex b/extra_credit/equations/costgrad.tex
index 5537f3d..40b8c6b 100644
--- a/extra_credit/equations/costgrad.tex
+++ b/extra_credit/equations/costgrad.tex
@@ -1,2 +1,2 @@
-\frac{\partial J}{\partial a_{i}}=1/m\sum_{k=1}^{N}\left(\sigma(t_{k})-y_{k}\right)x_{k}^{i}
+\frac{\partial J}{\partial a_{k}}=\sum_{i=1}^{N}\left(\sigma(t_{k})-y_{k}\right)x_{i}^{k}
 
diff --git a/extra_credit/equations/sigma.png b/extra_credit/equations/sigma.png
index ca351f1..2648705 100644
Binary files a/extra_credit/equations/sigma.png and b/extra_credit/equations/sigma.png differ
diff --git a/extra_credit/equations/t.png b/extra_credit/equations/t.png
index 2aad89f..190ad7c 100644
Binary files a/extra_credit/equations/t.png and b/extra_credit/equations/t.png differ
diff --git a/extra_credit/equations/x.png b/extra_credit/equations/x.png
index 6394239..d6d08d8 100644
Binary files a/extra_credit/equations/x.png and b/extra_credit/equations/x.png differ