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

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Final answer to the problem

$\frac{-2}{3\sqrt[3]{x^{5}}}$
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Step-by-step Solution

How should I solve this problem?

  • Find the derivative
  • 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
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

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

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

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Learn how to solve problems step by step online. Find the derivative d/dx(x^(-2/3)) using the power rule. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Multiplying fractions -\frac{2}{3} \times \frac{1}{x^{\left|-\frac{5}{3}\right|}}. Multiplying fractions -\frac{2}{3} \times \frac{1}{\sqrt[3]{x^{5}}}.

Final answer to the problem

$\frac{-2}{3\sqrt[3]{x^{5}}}$

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Function Plot

Plotting: $\frac{-2}{3\sqrt[3]{x^{5}}}$

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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

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