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Find the derivative $\frac{d}{dy}\left(y^{-\frac{1}{2}}\right)$ using the power rule

Step-by-step Solution

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Final Answer

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

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Simplifying

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

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

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Learn how to solve problems step by step online. Find the derivative d/dy(y^(-1/2)) 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{1}{2} and -1. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

Final Answer

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

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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

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Function Plot

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

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1
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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

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