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Mathematics
Mathematics
Problem
If
y
=
x
+
[
x
]
y = x + [x]
y
=
x
+
[
x
]
, then a. Statement I
d
y
d
x
=
1
\frac{dy}{dx} = 1
d
x
d
y
=
1
for all
x
∈
R
x \in R
x
∈
R
b. Statement II
d
(
[
x
]
)
d
x
=
{
0
,
x
∉
Integer
does not exist
,
x
∈
Integer
\frac{d([x])}{dx} = \begin{cases} 0, & x \notin \text{Integer} \\ \text{does not exist}, & x \in \text{Integer} \end{cases}
d
x
d
([
x
])
=
{
0
,
does not exist
,
x
∈
/
Integer
x
∈
Integer
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