# Step-by-step Solution

Go!
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## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(\left(x^3+2\right)^2\left(x^5+4\right)^4\right)$

Solving method

Learn how to solve definite integrals problems step by step online.

$\frac{d}{dx}\left(\left(x^3+2\right)^2\right)\left(x^5+4\right)^4+\left(x^3+2\right)^2\frac{d}{dx}\left(\left(x^5+4\right)^4\right)$

Learn how to solve definite integrals problems step by step online. Find the derivative using the product rule (d/dx)((x^3+2)^2(x^5+4)^4). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x^3+2\right)^2 and g=\left(x^5+4\right)^4. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two functions is the sum of the derivatives of each function.

## Final Answer

$\left(6x^{7}+24x^2+20x^3x^{4}+40x^{4}\right)\left(x^5+4\right)^{3}\left(x^3+2\right)$
SnapXam A2
Answer Assistant

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a
b
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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

### Tips on how to improve your answer:

$\frac{d}{dx}\left(\left(x^3+2\right)^2\left(x^5+4\right)^4\right)$

### Main topic:

Definite Integrals

~ 1.93 s