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Find the derivative using the product rule $c=\frac{\left(q+2\right)^{\left(3q+1\right)}\left(q-1\right)}{\left(3-q\right)\left(2q+4\right)}$

Step-by-step Solution

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Final answer to the problem

$c=\frac{\left(q+2\right)^{3q}\left(q-1\right)}{2\left(3-q\right)}$
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Step-by-step Solution

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Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$

$c=\frac{\left(q-1\right)\left(q+2\right)^{3q}\left(q+2\right)^1}{\left(3-q\right)\left(2q+4\right)}$

Learn how to solve combining like terms problems step by step online.

$c=\frac{\left(q-1\right)\left(q+2\right)^{3q}\left(q+2\right)^1}{\left(3-q\right)\left(2q+4\right)}$

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Learn how to solve combining like terms problems step by step online. Find the derivative using the product rule c=((q+2)^(3q+1)(q-1))/((3-q)(2q+4)). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Any expression to the power of 1 is equal to that same expression. When multiplying exponents with same base you can add the exponents: \left(q+2\right)^{3q}\left(q+2\right)\left(q-1\right). Simplify the derivative.

Final answer to the problem

$c=\frac{\left(q+2\right)^{3q}\left(q-1\right)}{2\left(3-q\right)}$

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Function Plot

Plotting: $c+\frac{-\left(q+2\right)^{\left(3q+1\right)}q+\left(q+2\right)^{\left(3q+1\right)}}{\left(3-q\right)\left(2q+4\right)}$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Combining like terms

Algebraic expressions can be simplified by combining like terms.

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