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Find the derivative of $\frac{x^4-4x^3-4x^2}{x+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}}$

Step-by-step Solution

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Final Answer

$\frac{24\left(4x^{3}-12x^{2}-8x\right)\left(4\left(3x^2+2x^3\right)+6x^4+24x\right)-24\left(x^4-4x^3-4x^2\right)\left(4\left(6x+6x^{2}\right)+24x^{3}+24\right)}{\left(4\left(3x^2+2x^3\right)+6x^4+24x\right)^2}$
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Step-by-step Solution

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Combine fractions with different denominator using the formula: $\displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}$

$\frac{d}{dx}\left(\frac{x^4-4x^3-4x^2}{\frac{3x^2+2x^3}{6}+x+\frac{x^4}{4}}\right)$

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$\frac{d}{dx}\left(\frac{x^4-4x^3-4x^2}{\frac{3x^2+2x^3}{6}+x+\frac{x^4}{4}}\right)$

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Learn how to solve problems step by step online. Find the derivative of (x^4-4x^3-4x^2)/(x+(x^2)/2(x^3)/3(x^4)/4). Combine fractions with different denominator using the formula: \displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}. Combine fractions with different denominator using the formula: \displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}. Combine \frac{4\left(3x^2+2x^3\right)+6x^4}{24}+x in a single fraction. Divide fractions \frac{x^4-4x^3-4x^2}{\frac{4\left(3x^2+2x^3\right)+6x^4+24x}{24}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.

Final Answer

$\frac{24\left(4x^{3}-12x^{2}-8x\right)\left(4\left(3x^2+2x^3\right)+6x^4+24x\right)-24\left(x^4-4x^3-4x^2\right)\left(4\left(6x+6x^{2}\right)+24x^{3}+24\right)}{\left(4\left(3x^2+2x^3\right)+6x^4+24x\right)^2}$

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Function Plot

Plotting: $\frac{24\left(4x^{3}-12x^{2}-8x\right)\left(4\left(3x^2+2x^3\right)+6x^4+24x\right)-24\left(x^4-4x^3-4x^2\right)\left(4\left(6x+6x^{2}\right)+24x^{3}+24\right)}{\left(4\left(3x^2+2x^3\right)+6x^4+24x\right)^2}$

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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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