Repository: sympy/sympy

Issue:
Laplace transform of derivatives rule does not handle coefficients
I believe there is new support for:
```
from sympy import Function, laplace_transform
from sympy.abc import s,t
x = Function('x')
laplace_transform(x(t).diff(t),t,s)
```
(which gives: `s*LaplaceTransform(x(t), t, s) - x(0)` as expected)

However the following result is incorrect in sympy 1.10.1

```
laplace_transform(10*x(t).diff(t),t,s)
```
(which also gives `s*LaplaceTransform(x(t), t, s) - x(0)` instead of 10 times that)



Discussion:

Patch:
diff --git a/.mailmap b/.mailmap
index ee94aa49dc..1b21777276 100644
--- a/.mailmap
+++ b/.mailmap
@@ -510,6 +510,7 @@ JMSS-Unknown <31131631+JMSS-Unknown@users.noreply.github.com>
 Jack Kemp <metaknightdrake-git@yahoo.co.uk>
 Jack Kemp <metaknightdrake-git@yahoo.co.uk> <kempj@tplxdt003.nat.physics.ox.ac.uk>
 Jack McCaffery <jpmccaffery@gmail.com>
+Jack Schmidt <1107865+jackschmidt@users.noreply.github.com>
 Jacob Garber <jgarber1@ualberta.ca>
 Jai Luthra <me@jailuthra.in>
 Jaime R <38530589+Jaime02@users.noreply.github.com>
diff --git a/sympy/integrals/transforms.py b/sympy/integrals/transforms.py
index 33084acd3f..4ec6007739 100644
--- a/sympy/integrals/transforms.py
+++ b/sympy/integrals/transforms.py
@@ -1738,7 +1738,7 @@ def _laplace_rule_diff(f, t, s, doit=True, **hints):
             d.append(s**(ma1[n]-k-1)*y)
         r = s**ma1[n]*_laplace_apply_rules(ma1[g].func(t), t, s, doit=doit,
                                            **hints)
-        return r - Add(*d)
+        return ma1[a]*(r - Add(*d))
     return None
 
 


Test patch:
diff --git a/sympy/integrals/tests/test_transforms.py b/sympy/integrals/tests/test_transforms.py
index c16e0f942c..87efcb2acb 100644
--- a/sympy/integrals/tests/test_transforms.py
+++ b/sympy/integrals/tests/test_transforms.py
@@ -699,6 +699,9 @@ def test_laplace_transform():
     assert LT(diff(f(t), (t, 3)), t, s) == s**3*LaplaceTransform(f(t), t, s)\
         - s**2*f(0) - s*Subs(Derivative(f(t), t), t, 0)\
             - Subs(Derivative(f(t), (t, 2)), t, 0)
+    # Issue #23307
+    assert LT(10*diff(f(t), (t, 1)), t, s) == 10*s*LaplaceTransform(f(t), t, s)\
+        - 10*f(0)
     assert LT(a*f(b*t)+g(c*t), t, s) == a*LaplaceTransform(f(t), t, s/b)/b +\
         LaplaceTransform(g(t), t, s/c)/c
     assert inverse_laplace_transform(