state the current law
Answers
Answer:
Gustav Kirchhoff's current law is one of the fundamental laws used for circuit analysis.his current law States that for a parael path the total current entering a circuits junction is exactly equal to the total current leaving the same junction
Answer:
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Explanation:
Looking at the equation,
f
(
x
)
=
(
2
x
−
3
)
4
(
x
2
+
x
+
1
)
5
we first notice a couple patterns.
1. The function is a product of two terms
2. Each of the terms is a term with an exponent .
Since the function is a product of two terms, we know that we have to use the Product Rule to find the first derivative. The Product Rule states,
For an equation,
f
(
x
)
=
g
(
x
)
⋅
h
(
x
)
f
'
(
x
)
=
g
'
(
x
)
h
(
x
)
+
g
(
x
)
h
'
(
x
)
In our case,
f
(
x
)
=
g
(
x
)
⋅
h
(
x
)
where,
g
(
x
)
=
(
2
x
−
3
)
4
h
(
x
)
=
(
x
2
+
x
+
1
)
5
Now we need to calculate g'(x) and h'(x) for the product rule. For this, we need the Chain Rule. It states,
If
F
(
x
)
=
f
(
g
(
x
)
)
,
F
'
(
x
)
=
f
'
(
g
(
x
)
)
⋅
g
'
(
x
)
so, in our specific case,
g
(
x
)
=
(
2
x
−
3
)
4
g
'
(
x
)
=
4
(
2
x
−
3
)
3
⋅
(
2
)
h
(
x
)
=
(
x
2
+
x
+
1
)
5
h
'
(
x
)
=
5
(
x
2
+
x
+
1
)
4
⋅
(
2
x
+
1
)
Therefore,
f
'
(
x
)
=
g
'
(
x
)
h
(
x
)
+
g
(
x
)
h
'
(
x
)
=
8
⋅
(
2
x
−
3
)
3
⋅
(
x
2
+
x
+
1
)
5
+
(
2
x
−
3
)
4
⋅
5
(
x
2
+
x
+
1
)
4
⋅
(
2
x
+
1
)
=
(
2
x
−
3
)
3
(
8
⋅
(
x
2
+
x
+
1
)
5
+
(
2
x
−
3
)
⋅
5
(
x
2
+
x
+
1
)
4
⋅
(
2
x
+
1
)
)
=
(
2
x
−
3
)
3
⋅
(
x
2
+
x
+
1
)
4
⋅
(
8
(
x
2
+
x
+
1
)
+
5
(
2
x
−
3
)
(
2
x
+
1
)
)
=
(
2
x
−
3
)
3
⋅
(
x
2
+
x
+
1
)
4
⋅
(
8
x
2
+
8
x
+
8
+
5
(
4
x
2
−
x
−
3
)
)
=
(
2
x
−
3
)
3
⋅
(
x
2
+
x
+
1
)
4
⋅
(
8
x
2
+
8
x
+
8
+
20
x
2
−
5
x
−
15
)
=
(
2
x
−
3
)
3
(
x
2
+
x
+
1
)
4
(
28
x
2
−
12
x
−
7
)
□