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Find the derivative of $\sqrt[3]{4x^2+3x+1}$

Step-by-step Solution

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Solution

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Final Answer

$\frac{\frac{1}{3}}{\sqrt[3]{\left(4x^2+3x+1\right)^{2}}}\left(8x+3\right)$
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Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(\sqrt[3]{4x^2+3x+1}\right)$

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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{1}{3}\left(4x^2+3x+1\right)^{-\frac{2}{3}}\frac{d}{dx}\left(4x^2+3x+1\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{1}{3}\left(4x^2+3x+1\right)^{-\frac{2}{3}}\frac{d}{dx}\left(4x^2+3x+1\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of (4x^2+3x+1)^1/3. 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 derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero. The derivative of the linear function times a constant, is equal to the constant.

Final Answer

$\frac{\frac{1}{3}}{\sqrt[3]{\left(4x^2+3x+1\right)^{2}}}\left(8x+3\right)$

Explore different ways to solve this problem

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

Find the derivativeFind d/dx((4x^2+3x+1)^1/3) using the product ruleFind d/dx((4x^2+3x+1)^1/3) using the quotient ruleFind d/dx((4x^2+3x+1)^1/3) using logarithmic differentiationFind d/dx((4x^2+3x+1)^1/3) using the definition

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(◻)
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◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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:

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Main topic:

Differential Calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.11 s

Related topics:

Differential CalculusCalculusPower Rule for DerivativesBasic Differentiation RulesSum Rule of DifferentiationConstant Rule for Differentiation

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