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Find the derivative $\frac{d}{dx}\left(\sqrt[3]{x}+\sqrt{x}\right)$ using the sum rule

Step-by-step Solution

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Final Answer

$\frac{2+3\sqrt[6]{x}}{6\sqrt[3]{x^{2}}}$
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Step-by-step Solution

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The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(\sqrt[3]{x}\right)+\frac{d}{dx}\left(\sqrt{x}\right)$

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

$\frac{d}{dx}\left(\sqrt[3]{x}\right)+\frac{d}{dx}\left(\sqrt{x}\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(x^1/3+x^1/2) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

Final Answer

$\frac{2+3\sqrt[6]{x}}{6\sqrt[3]{x^{2}}}$

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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

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Plotting: $\frac{2+3\sqrt[6]{x}}{6\sqrt[3]{x^{2}}}$

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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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