What is the derivative of x^{1/6} ?

The derivative of x^{1/6} is 1/(6x^{5/6)}

What is the first derivative of x^{1/6} ?

The first derivative of x^{1/6} is 1/(6x^{5/6)}

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derivative of

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

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

Solution steps

\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}}}

\frac{d}{d x} (- x^{2} + 13 x - 22)

\int e^{t - s t}

g (x) = 10 x e^{3 - x^{2}}

7 t \cdot y^{^{'}} - 5 y = t

4 y^{^{''}} - y = 1, y (0) = 0, y^{^{'}} (0) = \frac{1}{2}

What is the derivative of x^{1/6} ?
The derivative of x^{1/6} is 1/(6x^{5/6)}
What is the first derivative of x^{1/6} ?
The first derivative of x^{1/6} is 1/(6x^{5/6)}