What is (\partial)/(\partial x)(3/(\sqrt[3]{x)}) ?

The answer to (\partial)/(\partial x)(3/(\sqrt[3]{x)}) is -1/(x^{4/3)}

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(\partial)/(\partial x)(3/(\sqrt[3]{x)})

- \frac{1}{x ^{\frac{4}{3}}}

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 3 \frac{\partial}{\partial x} (x^{- \frac{1}{3}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 3 (- \frac{1}{3} x^{- \frac{1}{3} - 1})

Simplify

3 (- \frac{1}{3} x^{- \frac{1}{3} - 1}) : - \frac{1}{x ^{\frac{4}{3}}}

= - \frac{1}{x ^{\frac{4}{3}}}

x \to 2 lim (\frac{0}{x - 2})

n = 1 \sum \infty n^{3} \cdot 2^{- n}

\frac{d y}{d t} = y + \frac{3}{y ^{2}}

(\frac{x ^{2} + 2}{x ^{2} - 2})^{4}

\frac{1}{( 3 x + 1 )}

What is (\partial)/(\partial x)(3/(\sqrt[3]{x)}) ?
The answer to (\partial)/(\partial x)(3/(\sqrt[3]{x)}) is -1/(x^{4/3)}