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Find the derivative using logarithmic differentiation method $y=\sqrt[3]{\frac{x\left(x-6\right)}{x^2+2}}$

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Solution

Formulas

Videos

Calculus: Derivatives 2 | Taking derivatives | Differential Calculus | Khan Academy

https://www.youtube.com/watch?v=ay8838UZ4nM

Pre-Calculus - Using the square root method to solve a quadratic equation, (1/2)x^2 + 3 = 19

https://www.youtube.com/watch?v=dvE_W89LrqA

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

Algebra 2 - Dividing two rational expressions by factoring, ((x + y)/6) / ((x^2 - y^2)/3)

https://www.youtube.com/watch?v=mAn_OHWNj2c

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=mSVrqKZDRF4

Worked example: Evaluating derivative with implicit differentiation | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=KyYC8XzKsHU

Function Plot

Plotting: $\frac{1}{3}\left(\frac{1}{x}+\frac{1}{x-6}+\frac{-2x}{x^2+2}\right)\sqrt[3]{\frac{x\left(x-6\right)}{x^2+2}}$

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7
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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
D□x
∫
∫◻
|◻|
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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Similar Problems Solved

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Find the derivative

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

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

See formulas (6)

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