What is (\partial)/(\partial x)((\sqrt[7]{x})^4) ?

The answer to (\partial)/(\partial x)((\sqrt[7]{x})^4) is 4/(7x^{3/7)}

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(\partial)/(\partial x)((\sqrt[7]{x})^4)

\frac{\partial}{\partial x} ((7 x)^{4})

\frac{4}{7 x ^{\frac{3}{7}}}

Solution steps

\frac{\partial}{\partial x} ((7 x)^{4})

Simplify

(7 x)^{4} : x^{\frac{4}{7}}

= \frac{\partial}{\partial x} (x^{\frac{4}{7}})

Apply the Power Rule:

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

= \frac{4}{7} x^{\frac{4}{7} - 1}

Simplify

\frac{4}{7} x^{\frac{4}{7} - 1} : \frac{4}{7 x ^{\frac{3}{7}}}

= \frac{4}{7 x ^{\frac{3}{7}}}

x \to 0 + lim ((- ln (x))^{x})

\frac{d y}{d x} = \frac{( 3 x ^{2} )}{y ^{2}}

\frac{d}{d x} (x - sin (2 x))

x \to - 2 lim (x (2))

\frac{\partial}{\partial y} (2 e^{x})

What is (\partial)/(\partial x)((\sqrt[7]{x})^4) ?
The answer to (\partial)/(\partial x)((\sqrt[7]{x})^4) is 4/(7x^{3/7)}