What is the derivative of f(x)=\sqrt[6]{x} ?

The derivative of f(x)=\sqrt[6]{x} is 1/(6x^{5/6)}

What is the first derivative of f(x)=\sqrt[6]{x} ?

The first derivative of f(x)=\sqrt[6]{x} is 1/(6x^{5/6)}

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derivative of

f (x) = 6 x

\frac{1}{6 x ^{\frac{5}{6}}}

Solution steps

\frac{d}{d x} (6 x)

Apply radical rule:

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

= \frac{d}{d x} (x^{\frac{1}{6}})

Apply the Power Rule:

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

= \frac{1}{6} x^{\frac{1}{6} - 1}

Simplify

\frac{1}{6} x^{\frac{1}{6} - 1} : \frac{1}{6 x ^{\frac{5}{6}}}

= \frac{1}{6 x ^{\frac{5}{6}}}

\int_{0}^{1} \frac{x + 1}{x ^{2} + 2 x - 3} d x

\frac{d}{d x} (a x^{2} (x - 4) + b x^{4} ln (\frac{x}{4}))

\int x^{4} ln (x^{5}) d x

\frac{d y}{d x} = 2 y - x y^{2}

\frac{d}{d x} ((2 x - 1) sin (x - 2))

What is the derivative of f(x)=\sqrt[6]{x} ?
The derivative of f(x)=\sqrt[6]{x} is 1/(6x^{5/6)}
What is the first derivative of f(x)=\sqrt[6]{x} ?
The first derivative of f(x)=\sqrt[6]{x} is 1/(6x^{5/6)}