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\frac{d}{dx}\left(\frac{-6}{\left(5x-1\right)^{\frac{1}{3}}}\right)

Derive the function -6/((5x-1)^(1/3)) with respect to x

Answer

$\frac{10}{\sqrt[3]{\left(5x-1\right)^{4}}}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\frac{-6}{\left(5x-1\right)^{\frac{1}{3}}}\right)$
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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{6\frac{d}{dx}\left(\sqrt[3]{5x-1}\right)+\sqrt[3]{5x-1}\cdot\frac{d}{dx}\left(-6\right)}{\left(\sqrt[3]{5x-1}\right)^2}$

Unlock this step-by-step solution!

Answer

$\frac{10}{\sqrt[3]{\left(5x-1\right)^{4}}}$
$\frac{d}{dx}\left(\frac{-6}{\left(5x-1\right)^{\frac{1}{3}}}\right)$

Main topic:

Differential calculus

Used formulas:

3. See formulas

Time to solve it:

~ 0.43 seconds