# Step-by-step Solution

Go!
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## Final Answer

$\frac{-\frac{1}{2}}{\sqrt{y^{3}}}$
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## Step-by-step Solution

Problem to solve:

$\frac{d}{dy}\left(y^{\left(-1\right)\cdot\frac{1}{2}}\right)$

Solving method

1

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

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

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

$\frac{-\frac{1}{2}}{\sqrt{y^{3}}}$

## Final Answer

$\frac{-\frac{1}{2}}{\sqrt{y^{3}}}$
SnapXam A2
Answer Assistant

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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

### Tips on how to improve your answer:

$\frac{d}{dy}\left(y^{\left(-1\right)\cdot\frac{1}{2}}\right)$

### Main topic:

Power Rule for Derivatives

~ 0.25 s