# Step-by-step Solution

## Find the derivative using the product rule $\frac{d}{dx}\left(\left(2-x\right)^3\left(1-x^2\right)^2\right)$

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$-3\left(2-x\right)^{2}\left(1-x^2\right)^2-4x\left(2-x\right)^3\left(1-x^2\right)$

## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(\left(2-x\right)^3\left(1-x^2\right)^2\right)$

Choose the solving method

1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\left(2-x\right)^3$ and $g=\left(1-x^2\right)^2$

$\frac{d}{dx}\left(\left(2-x\right)^3\right)\left(1-x^2\right)^2+\left(2-x\right)^3\frac{d}{dx}\left(\left(1-x^2\right)^2\right)$

Learn how to solve product rule of differentiation problems step by step online.

$\frac{d}{dx}\left(\left(2-x\right)^3\right)\left(1-x^2\right)^2+\left(2-x\right)^3\frac{d}{dx}\left(\left(1-x^2\right)^2\right)$

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)((2-x)^3(1-x^2)^2). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(2-x\right)^3 and g=\left(1-x^2\right)^2. 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 or more functions is the sum of the derivatives of each function.

$-3\left(2-x\right)^{2}\left(1-x^2\right)^2-4x\left(2-x\right)^3\left(1-x^2\right)$
SnapXam A2

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7
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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

$\frac{d}{dx}\left(\left(2-x\right)^3\left(1-x^2\right)^2\right)$