👉 Try now NerdPal! Our new math app on iOS and Android

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

Step-by-step Solution

Go!
Math mode
Text mode
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
|◻|
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

Final Answer

$-\frac{3}{2}+3x-\frac{3}{2}x^2$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

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 differential calculus problems step by step online.

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

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve differential calculus problems step by step online. Find the derivative using the product rule d/dx(((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. Divide 1 by 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 derivative of a sum of two or more functions is the sum of the derivatives of each function.

Final Answer

$-\frac{3}{2}+3x-\frac{3}{2}x^2$

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

Find the derivativeFind derivative of ((1+-1x)^3)/2 using the quotient ruleFind derivative of ((1+-1x)^3)/2 using logarithmic differentiationFind derivative of ((1+-1x)^3)/2 using the definition

Give us your feedback!

Function Plot

Plotting: $-\frac{3}{2}+3x-\frac{3}{2}x^2$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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
|◻|
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

How to improve your answer:

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your Subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account