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# Find the derivative $\frac{d}{dx}\left(\frac{1}{\sqrt{x}-1}\right)$

## Step-by-step Solution

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###  Videos

$\frac{-\frac{1}{2}}{\left(\sqrt{x}-1\right)^2\sqrt{x}}$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(\frac{1}{\sqrt{x}-1}\right)$

Specify the solving method

1

Apply the quotient rule for differentiation, which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

Learn how to solve quotient rule of differentiation problems step by step online.

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

Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx(1/(x^1/2-1)). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The derivative of the constant function (1) is equal to zero. Any expression multiplied by 0 is equal to 0. x+0=x, where x is any expression.

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

##  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

Find the derivativeFind derivative of 1/(x^0.5-1) using the product ruleFind derivative of 1/(x^0.5-1) using the quotient ruleFind derivative of 1/(x^0.5-1) using logarithmic differentiationFind derivative of 1/(x^0.5-1) using the definition

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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

### Main topic:

Quotient Rule of Differentiation

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