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

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

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

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

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derivative of

ln (6 x)

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (6 x) = \frac{1}{6 x ^{\frac{5}{6}}}

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

Simplify

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

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

(x + y + 4 d x) + (2 x + 2 y + 1 d y) = 0

f (x) = 4 e^{x} + x, (0, 4)

\frac{\partial}{\partial x} (\frac{1}{3} t^{6} - 6 t^{4} + t)

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

\int arctan (1) d x

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