What is (\partial)/(\partial x)(x^{1/4}) ?

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

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(\partial)/(\partial x)(x^{1/4})

\frac{\partial}{\partial x} (x^{\frac{1}{4}})

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

Solution steps

\frac{\partial}{\partial x} (x^{\frac{1}{4}})

Apply the Power Rule:

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

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

Simplify

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

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

x \to 1 lim (2 x + 3)

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\frac{d}{d x} (\frac{5 x ^{3}}{4} - \frac{2}{5 x ^{3}})

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