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Find the derivative using the quotient rule $\frac{d}{dx}\left(\frac{\frac{\frac{a}{\sqrt{3}}}{\left(\sqrt{3}bx-x^2\right)^{\frac{5}{3}}}}{\sqrt[3]{\left(\sqrt{3}b+4x\right)^{2}}}\right)$

Step-by-step Solution

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Final Answer

$\frac{-\sqrt{3}\left(5\left(\sqrt{3}b+4x\right)\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{2}}\left(\sqrt{3}b-2x\right)+8\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{5}}\right)a}{9\sqrt[3]{\left(\sqrt{3}b+4x\right)^{5}}\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{10}}}$
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Step-by-step Solution

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$\frac{d}{dx}\left(\frac{\frac{\frac{a}{\sqrt{3}}}{\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{5}}}}{\sqrt[3]{\left(\sqrt{3}b+4x\right)^{2}}}\right)$

Learn how to solve integrals of rational functions problems step by step online.

$\frac{d}{dx}\left(\frac{\frac{\frac{a}{\sqrt{3}}}{\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{5}}}}{\sqrt[3]{\left(\sqrt{3}b+4x\right)^{2}}}\right)$

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Learn how to solve integrals of rational functions problems step by step online. Find the derivative using the quotient rule d/dx(((a/(3^1/2))/((3^1/2bx-x^2)^(5/3)))/((3^1/2b+4x)^2/3)). Simplifying. Simplifying. 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}}. The power of a product is equal to the product of it's factors raised to the same power.

Final Answer

$\frac{-\sqrt{3}\left(5\left(\sqrt{3}b+4x\right)\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{2}}\left(\sqrt{3}b-2x\right)+8\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{5}}\right)a}{9\sqrt[3]{\left(\sqrt{3}b+4x\right)^{5}}\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{10}}}$

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Function Plot

Plotting: $\frac{-\sqrt{3}\left(5\left(\sqrt{3}b+4x\right)\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{2}}\left(\sqrt{3}b-2x\right)+8\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{5}}\right)a}{9\sqrt[3]{\left(\sqrt{3}b+4x\right)^{5}}\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{10}}}$

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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

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