What is the derivative of \sqrt[k]{x} ?

The derivative of \sqrt[k]{x} is (x^{(1-k)/k})/(k)

What is the first derivative of \sqrt[k]{x} ?

The first derivative of \sqrt[k]{x} is (x^{(1-k)/k})/(k)

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\frac{x ^{\frac{1 - k}{k}}}{k}

Solution steps

Apply radical rule:

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{k} x^{\frac{1}{k} - 1} : \frac{x ^{\frac{1 - k}{k}}}{k}

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

\frac{x ^{5} - 5}{x + 1}

x \to 4 lim (9 x + ∣ x - 4 ∣)

x d y + y d x = 3 d x

\frac{1 - cos ( x )}{sin ( x )}

y^{^{'}} + \frac{3 x}{x ^{2} + 4} y = \frac{x}{x ^{2} + 4}, y (0) = 1

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