diff --git a/pkgs/development/compilers/cudatoolkit/common.nix b/pkgs/development/compilers/cudatoolkit/common.nix
index 585277064ab1..f408d7b33121 100644
--- a/pkgs/development/compilers/cudatoolkit/common.nix
+++ b/pkgs/development/compilers/cudatoolkit/common.nix
@@ -100,14 +100,14 @@ stdenv.mkDerivation rec {
       mv * $out/
     ''}
     ${lib.optionalString (lib.versionAtLeast version "11") ''
-      mkdir -p $out/bin $out/lib64 $out/include $out/doc
+      mkdir -p $out/bin $out/lib64 $out/include $doc
       for dir in pkg/builds/* pkg/builds/cuda_nvcc/nvvm pkg/builds/cuda_cupti/extras/CUPTI; do
         if [ -d $dir/bin ]; then
           mv $dir/bin/* $out/bin
         fi
         if [ -d $dir/doc ]; then
-          (cd $dir/doc && find . -type d -exec mkdir -p $out/doc/\{} \;)
-          (cd $dir/doc && find . \( -type f -o -type l \) -exec mv \{} $out/doc/\{} \;)
+          (cd $dir/doc && find . -type d -exec mkdir -p $doc/\{} \;)
+          (cd $dir/doc && find . \( -type f -o -type l \) -exec mv \{} $doc/\{} \;)
         fi
         if [ -L $dir/include ] || [ -d $dir/include ]; then
           (cd $dir/include && find . -type d -exec mkdir -p $out/include/\{} \;)
diff --git a/pkgs/development/compilers/cudatoolkit/default.nix b/pkgs/development/compilers/cudatoolkit/default.nix
index 1747f16f12d1..33a386cfb926 100644
--- a/pkgs/development/compilers/cudatoolkit/default.nix
+++ b/pkgs/development/compilers/cudatoolkit/default.nix
@@ -66,11 +66,18 @@ rec {
   };
 
   cudatoolkit_11_4 = common {
-    version = "11.4.1";
-    url = "https://developer.download.nvidia.com/compute/cuda/11.4.1/local_installers/cuda_11.4.1_470.57.02_linux.run";
-    sha256 = "0180pb1zfajb9l6blr467xkx01yp3snfwm2xix8x52crf6d36v6x";
+    version = "11.4.2";
+    url = "https://developer.download.nvidia.com/compute/cuda/11.4.2/local_installers/cuda_11.4.2_470.57.02_linux.run";
+    sha256 = "sha256-u9h8oOkT+DdFSnljZ0c1E83e9VUILk2G7Zo4ZZzIHwo=";
     gcc = gcc10; # can bump to 11 along with stdenv.cc
   };
 
-  cudatoolkit_11 = cudatoolkit_11_2;
+  cudatoolkit_11_5 = common {
+    version = "11.5.0";
+    url = "https://developer.download.nvidia.com/compute/cuda/11.5.0/local_installers/cuda_11.5.0_495.29.05_linux.run";
+    sha256 = "sha256-rgoWk9lJfPPYHmlIlD43lGNpANtxyY1Y7v2sr38aHkw=";
+    gcc = gcc10; # can bump to 11 along with stdenv.cc
+  };
+
+  cudatoolkit_11 = cudatoolkit_11_4;
 }
diff --git a/pkgs/development/libraries/science/math/cudnn/default.nix b/pkgs/development/libraries/science/math/cudnn/default.nix
index d2a5a8c2a790..3d4d4c21e5a1 100644
--- a/pkgs/development/libraries/science/math/cudnn/default.nix
+++ b/pkgs/development/libraries/science/math/cudnn/default.nix
@@ -1,4 +1,6 @@
-{ callPackage, cudatoolkit_10_0, cudatoolkit_10_1, cudatoolkit_10_2, cudatoolkit_11_0, cudatoolkit_11_1, cudatoolkit_11_2 }:
+{ callPackage, cudatoolkit_10_0, cudatoolkit_10_1, cudatoolkit_10_2, cudatoolkit_11_0, cudatoolkit_11_1, cudatoolkit_11_2
+, cudatoolkit_11_3, cudatoolkit_11_4
+}:
 
 let
   generic = args: callPackage (import ./generic.nix (removeAttrs args ["cudatoolkit"])) {
@@ -46,5 +48,13 @@ in rec {
     cudatoolkit = cudatoolkit_11_2;
   };
 
-  cudnn_cudatoolkit_11 = cudnn_cudatoolkit_11_2;
+  cudnn_cudatoolkit_11_3 = cudnn_cudatoolkit_11_0.override {
+    cudatoolkit = cudatoolkit_11_3;
+  };
+
+  cudnn_cudatoolkit_11_4 = cudnn_cudatoolkit_11_0.override {
+    cudatoolkit = cudatoolkit_11_4;
+  };
+
+  cudnn_cudatoolkit_11 = cudnn_cudatoolkit_11_4;
 }
diff --git a/pkgs/development/libraries/science/math/cutensor/default.nix b/pkgs/development/libraries/science/math/cutensor/default.nix
index b8f4475ce122..25633ca63e6b 100644
--- a/pkgs/development/libraries/science/math/cutensor/default.nix
+++ b/pkgs/development/libraries/science/math/cutensor/default.nix
@@ -14,8 +14,12 @@ rec {
   };
 
   cutensor_cudatoolkit_10_2 = cutensor_cudatoolkit_10_1.override {
+    version = "1.3.1.3";
     libPath = "lib/10.2";
     cudatoolkit = cudatoolkit_10_2;
+    # 1.3.1 is compatible with CUDA 11.0, 11.1, and 11.2:
+    # ephemeral doc at https://developer.nvidia.com/cutensor/downloads
+    sha256 = "sha256-mNlVnabB2IC3HnYY0mb06RLqQzDxN9ePGVeBy3hkBC8=";
   };
 
   cutensor_cudatoolkit_10 = cutensor_cudatoolkit_10_2;
@@ -41,5 +45,5 @@ rec {
     cudatoolkit = cudatoolkit_11_4;
   };
 
-  cutensor_cudatoolkit_11 = cutensor_cudatoolkit_11_2;
+  cutensor_cudatoolkit_11 = cutensor_cudatoolkit_11_4;
 }
diff --git a/pkgs/top-level/all-packages.nix b/pkgs/top-level/all-packages.nix
index 0ed423b6e573..d97f407163d7 100644
--- a/pkgs/top-level/all-packages.nix
+++ b/pkgs/top-level/all-packages.nix
@@ -4282,7 +4282,8 @@ with pkgs;
     cudatoolkit_11_1
     cudatoolkit_11_2
     cudatoolkit_11_3
-    cudatoolkit_11_4;
+    cudatoolkit_11_4
+    cudatoolkit_11_5;
 
   cudatoolkit = cudatoolkit_10;
 
@@ -4295,7 +4296,9 @@ with pkgs;
     cudnn_cudatoolkit_11
     cudnn_cudatoolkit_11_0
     cudnn_cudatoolkit_11_1
-    cudnn_cudatoolkit_11_2;
+    cudnn_cudatoolkit_11_2
+    cudnn_cudatoolkit_11_3
+    cudnn_cudatoolkit_11_4;
 
   cudnn = cudnn_cudatoolkit_10;