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

Step-by-step Solution

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$\frac{\frac{1}{2}}{\sqrt{x}}$
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 Step-by-step Solution 

Problem to solve:

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

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

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

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

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

Learn how to solve power rule for derivatives problems step by step online. Find the derivative d/dx(x^1/2) 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}. 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.

$\frac{\frac{1}{2}}{\sqrt{x}}$

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Find the derivativeFind d/dx(x^1/2) using the product ruleFind d/dx(x^1/2) using the quotient ruleFind d/dx(x^1/2) using logarithmic differentiationFind d/dx(x^1/2) using the definition

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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

Main topic:

Power Rule for Derivatives

~ 0.04 s

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