en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of \sqrt[n]{x}

Solution

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

Solution

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

Solution steps

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

Apply radical rule:

n a = a^{\frac{1}{n}}

= \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}

Graph

Popular Examples

limit as x approaches 2 of (7x^5-10x^4-13x+6)/(3x^2-6x-8)

x \to 2 lim (\frac{7 x ^{5} - 10 x ^{4} - 13 x + 6}{3 x ^{2} - 6 x - 8})

derivative of (x^2+1^{0.6})

\frac{d}{d x} ((x^{2} + 1)^{0.6})

integral of (ln(x))/(xsqrt(1+(ln(x))^2))

\int \frac{ln ( x )}{x 1 + ( ln ( x ) ) ^{2}} d x

d/(dt)(-8cos(t))

\frac{d}{d t} (- 8 cos (t))

derivative of ln((x+a/(sqrt(y))))

\frac{d}{d x} (ln (\frac{x + a}{y}))

Frequently Asked Questions (FAQ)

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