en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(2/3 x)^3

Solution

derivative of

f (x) = (\frac{2}{3} x)^{3}

Solution

\frac{8 x ^{2}}{9}

Solution steps

\frac{d}{d x} ((\frac{2}{3} x)^{3})

Apply the chain rule:

3 (\frac{2}{3} x)^{2} \frac{d}{d x} (\frac{2}{3} x)

= 3 (\frac{2}{3} x)^{2} \frac{d}{d x} (\frac{2}{3} x)

\frac{d}{d x} (\frac{2}{3} x) = \frac{2}{3}

= 3 (\frac{2}{3} x)^{2} \frac{2}{3}

Simplify

3 (\frac{2}{3} x)^{2} \frac{2}{3} : \frac{8 x ^{2}}{9}

= \frac{8 x ^{2}}{9}

Popular Examples

integral of (sqrt(t^4+7t))(4t^3+7)

\int (t^{4} + 7 t) (4 t^{3} + 7) d t

limit as x approaches-9 of (x^2-1)/(9-x)

x \to - 9 lim (\frac{x ^{2} - 1}{9 - x})

(\partial)/(\partial x)(yln(xy^2p^3))

\frac{\partial}{\partial x} (y ln (x y^{2} p^{3}))

limit as x approaches 0+of 3(x)^{x/2}

x \to 0 + lim (3 (x)^{\frac{x}{2}})

integral from 0 to 7 of 1/(sqrt(49-x^2))

\int_{0}^{7} \frac{1}{49 - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2/3 x)^3 ?
The derivative of f(x)=(2/3 x)^3 is (8x^2)/9
What is the first derivative of f(x)=(2/3 x)^3 ?
The first derivative of f(x)=(2/3 x)^3 is (8x^2)/9