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Find the derivative $\frac{d}{dx}\left(\frac{3x^{\frac{23}{3}}}{23}+\frac{9x^{\frac{11}{3}}}{11}+\frac{9x^{\frac{17}{3}}}{17}+\frac{3x^{\frac{5}{3}}}{5}\right)$ using the sum rule

Step-by-step Solution

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Final Answer

$\sqrt[3]{x^{20}}+3\sqrt[3]{x^{8}}+3\sqrt[3]{x^{14}}+\frac{1}{\log^{3}\left(10\right)}\sqrt[3]{x^{2}}$
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Step-by-step Solution

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$\frac{d}{dx}\left(\frac{3\sqrt[3]{x^{23}}}{23}+\frac{9\sqrt[3]{x^{11}}}{11}+\frac{9\sqrt[3]{x^{17}}}{17}+\frac{3\sqrt[3]{x^{5}}}{5}\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(\frac{3\sqrt[3]{x^{23}}}{23}+\frac{9\sqrt[3]{x^{11}}}{11}+\frac{9\sqrt[3]{x^{17}}}{17}+\frac{3\sqrt[3]{x^{5}}}{5}\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx((3x^(23/3))/23+(9x^(11/3))/11(9x^(17/3))/17(3x^(5/3))/5) using the sum rule. Simplifying. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (\frac{1}{23}) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (\frac{1}{11}) is equal to the constant times the derivative of the function.

Final Answer

$\sqrt[3]{x^{20}}+3\sqrt[3]{x^{8}}+3\sqrt[3]{x^{14}}+\frac{1}{\log^{3}\left(10\right)}\sqrt[3]{x^{2}}$

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Function Plot

Plotting: $\sqrt[3]{x^{20}}+3\sqrt[3]{x^{8}}+3\sqrt[3]{x^{14}}+\frac{1}{\log^{3}\left(10\right)}\sqrt[3]{x^{2}}$

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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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Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

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