What is (\partial)/(\partial x)(-4/(x^4\sqrt[4]{x)}) ?

The answer to (\partial)/(\partial x)(-4/(x^4\sqrt[4]{x)}) is (17)/(x^{21/4)}

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(\partial)/(\partial x)(-4/(x^4\sqrt[4]{x)})

\frac{17}{x ^{\frac{21}{4}}}

Solution steps

Simplify

= \frac{\partial}{\partial x} (- \frac{4}{x ^{\frac{17}{4}}})

Take the constant out:

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

= - 4 \frac{\partial}{\partial x} (\frac{1}{x ^{\frac{17}{4}}})

Apply exponent rule:

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

= - 4 \frac{\partial}{\partial x} (x^{- \frac{17}{4}})

Apply the Power Rule:

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

= - 4 (- \frac{17}{4} x^{- \frac{17}{4} - 1})

Simplify

- 4 (- \frac{17}{4} x^{- \frac{17}{4} - 1}) : \frac{17}{x ^{\frac{21}{4}}}

= \frac{17}{x ^{\frac{21}{4}}}

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What is (\partial)/(\partial x)(-4/(x^4\sqrt[4]{x)}) ?
The answer to (\partial)/(\partial x)(-4/(x^4\sqrt[4]{x)}) is (17)/(x^{21/4)}