Detailed solution to Problem Set 15 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.
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