What is the derivative of \sqrt[7]{t} ?

The derivative of \sqrt[7]{t} is 1/(7t^{6/7)}

What is the first derivative of \sqrt[7]{t} ?

The first derivative of \sqrt[7]{t} is 1/(7t^{6/7)}

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derivative of

\frac{1}{7 t ^{\frac{6}{7}}}

Solution steps

Apply radical rule:

= \frac{d}{d t} (t^{\frac{1}{7}})

Apply the Power Rule:

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

= \frac{1}{7} t^{\frac{1}{7} - 1}

Simplify

\frac{1}{7} t^{\frac{1}{7} - 1} : \frac{1}{7 t ^{\frac{6}{7}}}

= \frac{1}{7 t ^{\frac{6}{7}}}

f (x) = sin (9 ln (x))

y^{^{''}} + 4 y = sin (x), y (0) = 1, y^{^{'}} (0) = 4

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What is the derivative of \sqrt[7]{t} ?
The derivative of \sqrt[7]{t} is 1/(7t^{6/7)}
What is the first derivative of \sqrt[7]{t} ?
The first derivative of \sqrt[7]{t} is 1/(7t^{6/7)}