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

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##  Final answer to the problem

$\frac{-3}{2\sqrt{x^{5}}}$
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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
Can't find a method? Tell us so we can add it.
1

Simplifying

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

Learn how to solve power rule for derivatives problems step by step online.

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

Learn how to solve power rule for derivatives problems step by step online. Find the derivative d/dx(x^((1*-3)/2)) using the power rule. Simplifying. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Subtract the values -\frac{3}{2} and -1. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

##  Final answer to the problem

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

##  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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7
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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: Power Rule for Derivatives

The power rule is used to differentiate functions of the form f(x)=x^a, when a is a real number.