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\frac{d}{dx}\left(\frac{x^3}{\left(x+3\right)^{\frac{1}{3}}}\right)

Derive the function (x^3)/((x+3)^(1/3)) with respect to x

Answer

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

Step-by-step explanation

Problem

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

Applying the quotient rule 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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

Unlock this step-by-step solution!

Answer

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

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

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 1.1 seconds