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Find the derivative of $\sqrt{\frac{x-1}{x^4+1}}$

Step-by-step Solution

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Final Answer

$\frac{-3x^{4}+1+4x^{3}}{2\sqrt{\left(x^4+1\right)^{3}}\sqrt{x-1}}$
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Step-by-step Solution

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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\frac{d}{dx}\left(\frac{\sqrt{x-1}}{\sqrt{x^4+1}}\right)$

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$\frac{d}{dx}\left(\frac{\sqrt{x-1}}{\sqrt{x^4+1}}\right)$

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Learn how to solve problems step by step online. Find the derivative of ((x-1)/(x^4+1))^1/2. 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}. 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}}. Cancel exponents \frac{1}{2} and 2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

Final Answer

$\frac{-3x^{4}+1+4x^{3}}{2\sqrt{\left(x^4+1\right)^{3}}\sqrt{x-1}}$

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 ((x-1)/(x^4+1))^0.5 using the product ruleFind derivative of ((x-1)/(x^4+1))^0.5 using the quotient ruleFind derivative of ((x-1)/(x^4+1))^0.5 using logarithmic differentiationFind derivative of ((x-1)/(x^4+1))^0.5 using the definition

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Plotting: $\frac{-3x^{4}+1+4x^{3}}{2\sqrt{\left(x^4+1\right)^{3}}\sqrt{x-1}}$

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5
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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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