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Find the derivative using the product rule $y=i\sqrt{\frac{nx-1}{x+1}}$

Step-by-step Solution

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Final answer to the problem

$\frac{-\frac{1}{2}\sqrt{nx-1}i}{\sqrt{\left(x+1\right)^{3}}}$
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Step-by-step Solution

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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=

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

Learn how to solve definition of derivative problems step by step online.

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

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Learn how to solve definition of derivative problems step by step online. Find the derivative using the product rule y=i((nx-1)/(x+1))^1/2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. The derivative of the constant function (i) is equal to zero.

Final answer to the problem

$\frac{-\frac{1}{2}\sqrt{nx-1}i}{\sqrt{\left(x+1\right)^{3}}}$

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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

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

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Function Plot

Plotting: $\frac{-\frac{1}{2}\sqrt{nx-1}i}{\sqrt{\left(x+1\right)^{3}}}$

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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

How to improve your answer:

Main Topic: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

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