Step-by-step Solution

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

Go!
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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Step-by-step explanation

Problem to solve:

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

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

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

Unlock this full step-by-step solution!

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}. Subtract the values 3 and -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}.

Final Answer

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

Related formulas:

6. See formulas

Time to solve it:

~ 0.12 s (SnapXam)