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Find the derivative using the quotient rule $\frac{d}{dx}\left(\ln\left(\frac{x^3\sqrt{3e^x\cdot x^2}}{\left(x+1\right)^2\left(x-1\right)^3}\right)\right)$

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Calculus - Learn how to take derivative using quotient rule by simplifying first, f(x)=x(1- 4/(x+3))

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Calculus - Find the derivative of natural logarithm using product property, d(ln(2x))/dx

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Function Plot

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

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5
6
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

How to improve your answer:

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.

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