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

The derivative of x^{1/n} is (x^{(1-n)/n})/(n)

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

The first derivative of x^{1/n} is (x^{(1-n)/n})/(n)

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\frac{d}{d x} (x^{\frac{1}{n}})

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

Solution steps

\frac{d}{d x} (x^{\frac{1}{n}})

Apply the Power Rule:

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

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

Simplify

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

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

x + y e^{\frac{y}{x}} d x - x e^{\frac{y}{x}} d y = 0

\frac{\partial}{\partial u} (a u)

\int \frac{x}{e ^{x^{2} - 8}} d x

\frac{\partial}{\partial x} (2 z e^{x yz})

\frac{d}{d θ} (1 - sin (θ))

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