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5
c
2
d
(
9
c
2
d
2
−
4
c
3
d
−
2
)
5 c^{2} d\left(9 c^{2} d^{2}-4 c^{3} d-2\right)
5
c
2
d
(
9
c
2
d
2
−
4
c
3
d
−
2
)
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Math Problems
Calculus
Find derivatives of using multiple formulae
Full solution
Q.
5
c
2
d
(
9
c
2
d
2
−
4
c
3
d
−
2
)
5 c^{2} d\left(9 c^{2} d^{2}-4 c^{3} d-2\right)
5
c
2
d
(
9
c
2
d
2
−
4
c
3
d
−
2
)
Distribute Terms:
Distribute
5
c
2
d
5c^2d
5
c
2
d
to each term inside the parentheses.
\newline
5
c
2
d
(
9
c
2
d
2
)
=
45
c
4
d
3
5c^2d(9c^2d^2) = 45c^4d^3
5
c
2
d
(
9
c
2
d
2
)
=
45
c
4
d
3
,
\newline
5
c
2
d
(
−
4
c
3
d
)
=
−
20
c
5
d
2
5c^2d(-4c^3d) = -20c^5d^2
5
c
2
d
(
−
4
c
3
d
)
=
−
20
c
5
d
2
,
\newline
5
c
2
d
(
−
2
)
=
−
10
c
2
d
5c^2d(-2) = -10c^2d
5
c
2
d
(
−
2
)
=
−
10
c
2
d
;
Combine Results:
Combine the results from the distribution.
\newline
The expression simplifies to
45
c
4
d
3
−
20
c
5
d
2
−
10
c
2
d
45c^4d^3 - 20c^5d^2 - 10c^2d
45
c
4
d
3
−
20
c
5
d
2
−
10
c
2
d
;
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