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Find the derivative of $\left(2-x\right)^3\left(1-x^2\right)^2$

Step-by-step Solution

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Final Answer

$-3\left(2-x\right)^{2}\left(1-x^2\right)^2-4x\left(2-x\right)^3\left(1-x^2\right)$
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Step-by-step Solution

Problem to solve:

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

Specify 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 differential calculus 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 the first 3 steps of this solution!

Learn how to solve differential calculus problems step by step online. Find the derivative of (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.

Final Answer

$-3\left(2-x\right)^{2}\left(1-x^2\right)^2-4x\left(2-x\right)^3\left(1-x^2\right)$
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Got another answer? Verify it!

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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

Tips on how to improve your answer:

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

Main topic:

Differential Calculus

Related Formulas:

6. See formulas

Time to solve it:

~ 0.14 s