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Find the derivative of $\ln\left(\frac{x^3\sqrt{3e^x\cdot x^2}}{\left(x+1\right)^2\left(x-1\right)^3}\right)$

Step-by-step Solution

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Final Answer

$\frac{3}{x}+\frac{1}{2}+\frac{1}{x}+\frac{-2}{x+1}+\frac{-3}{x-1}$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(3\ln\left(x\right)+\frac{1}{2}x+\frac{1}{2}\ln\left(3x^2\right)-2\ln\left(x+1\right)-3\ln\left(x-1\right)\right)$

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$\frac{d}{dx}\left(3\ln\left(x\right)+\frac{1}{2}x+\frac{1}{2}\ln\left(3x^2\right)-2\ln\left(x+1\right)-3\ln\left(x-1\right)\right)$

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Learn how to solve problems step by step online. Find the derivative of ln((x^3(3e^xx^2)^1/2)/((x+1)^2(x-1)^3)). Simplify the derivative by applying the properties of logarithms. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1.

Final Answer

$\frac{3}{x}+\frac{1}{2}+\frac{1}{x}+\frac{-2}{x+1}+\frac{-3}{x-1}$

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 ln(x^33e^x^0.5/(x+1)^2(x-1)^3) using the product ruleFind derivative of ln(x^33e^x^0.5/(x+1)^2(x-1)^3) using the quotient ruleFind derivative of ln(x^33e^x^0.5/(x+1)^2(x-1)^3) using logarithmic differentiation

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Function Plot

Plotting: $\frac{3}{x}+\frac{1}{2}+\frac{1}{x}+\frac{-2}{x+1}+\frac{-3}{x-1}$

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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

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