diff --git a/R/trans-numeric.R b/R/trans-numeric.R
index cddeef2a..301e15b0 100644
--- a/R/trans-numeric.R
+++ b/R/trans-numeric.R
@@ -42,7 +42,9 @@ asinh_trans <- function() {
   trans_new(
     "asinh",
     transform = asinh,
-    inverse = sinh
+    inverse = sinh,
+    d_transform = function(x) 1 / sqrt(x^2 + 1),
+    d_inverse = cosh
   )
 }
 
diff --git a/tests/testthat/test-trans-numeric.R b/tests/testthat/test-trans-numeric.R
index 749b8743..a7f5cbf8 100644
--- a/tests/testthat/test-trans-numeric.R
+++ b/tests/testthat/test-trans-numeric.R
@@ -142,6 +142,15 @@ test_that("atanh_trans derivatives work", {
   expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
 })
 
+test_that("asinh_trans derivatives work", {
+  trans <- asinh_trans()
+  expect_equal(trans$d_transform(c(-1, 0, 1)), c(sqrt(2) / 2, 1, sqrt(2) / 2))
+  expect_equal(trans$d_inverse(c(-log(2), 0, log(2))), c(1.25, 1, 1.25))
+  x <- seq(-0.9, 0.9, length.out = 10)
+  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
+  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
+})
+
 test_that("boxcox_trans derivatives work", {
   trans <- boxcox_trans(p = 0, offset = 1)
   expect_equal(trans$d_transform(c(0, 1, 2)), c(1, 1/2, 1/3))