Detailed solution to Problem Set 10 Exercise 9
- Question:
- Find d(5 + 3√x).
- Solutions:
- You can use the somewhat obscure Root Rule
(d(m√u) =
m√u du/(mu)):
d(5 + 3√x) =
d(3√x) =
3 d(√x) =
3(√x dx/(2x)) =
3√x dx/(2x),
which you can write as
3 dx/(2√x)
or 3⁄2 x−½ dx
if you want.
- Or you can avoid the Root Rule
by treating
√x
as x½:
d(5 + 3x½) =
d(3x½) =
3 d(x½) =
3(½ x½−1 dx) =
3⁄2 x−½ dx,
which you can write as
3 dx/(2√x)
or
3√x dx/(2x)
if you want.
Go back to the the course homepage.
This web page was written by Toby Bartels, last edited on 2025 June 9.
Toby reserves no legal rights to it.
The permanent URI of this web page
is
https://tobybartels.name/MATH-1600/2025SS/ps10.9d/.
