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

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##  Final answer to the problem

$-\frac{3}{2}\left(1-x\right)^{2}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Find the derivative using the definition
• Find the derivative using the product rule
• Find the derivative using the quotient rule
• Find the derivative using logarithmic differentiation
• Find the derivative
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
Can't find a method? Tell us so we can add it.
1

The derivative of a function multiplied by a constant ($\frac{1}{2}$) is equal to the constant times the derivative of the function

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

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

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

Learn how to solve definite integrals problems step by step online. Find the derivative of ((1-x)^3)/2. The derivative of a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiply the fraction and term in 3\left(\frac{1}{2}\right)\left(1-x\right)^{2}\frac{d}{dx}\left(1-x\right). The derivative of a sum of two or more functions is the sum of the derivatives of each function.

##  Final answer to the problem

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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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
|◻|
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

###  Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b