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# Find the derivative $\frac{d}{dx}\left(\sqrt[3]{x}\right)$ using the power rule

## Step-by-step Solution

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###  Videos

$\frac{1}{3\sqrt[3]{x^{2}}}$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(\sqrt[3]{x}\right)$

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1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{1}{3}x^{-\frac{2}{3}}$
2

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{1}{3\sqrt[3]{x^{2}}}$

$\frac{1}{3\sqrt[3]{x^{2}}}$

##  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 d/dx(x^1/3) using the product ruleFind d/dx(x^1/3) using the quotient ruleFind d/dx(x^1/3) using logarithmic differentiationFind d/dx(x^1/3) using the definition

SnapXam A2

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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

### Main topic:

Power Rule for Derivatives

~ 0.04 s

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