en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of \sqrt[3]{x^2+3}

Solution

Solution

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

Solution steps

Apply the chain rule:

\frac{1}{3 ( x ^{2} + 3 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} + 3)

= \frac{1}{3 ( x ^{2} + 3 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} + 3)

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

= \frac{1}{3 ( x ^{2} + 3 ) ^{\frac{2}{3}}} \cdot 2 x

Simplify

\frac{1}{3 ( x ^{2} + 3 ) ^{\frac{2}{3}}} \cdot 2 x : \frac{2 x}{3 ( x ^{2} + 3 ) ^{\frac{2}{3}}}

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

Popular Examples

(dy)/(dx)=9.8-0.2y

\frac{d y}{d x} = 9.8 - 0.2 y

derivative of y=arctan(2-x)derivative of

y = arctan (2 - x)

laplacetransform (2+t)^4 laplace transform

(2 + t)^{4}

derivative of (x*cos(x-2pi)/(x-2pi))

\frac{d}{d x} (\frac{x \cdot cos ( x ) - 2 π}{x - 2 π})

integral of 16sqrt(3)cos^4(3x)sin^2(3x)

\int 163 cos^{4} (3 x) sin^{2} (3 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{x^2+3} ?
The derivative of \sqrt[3]{x^2+3} is (2x)/(3(x^2+3)^{2/3)}
What is the first derivative of \sqrt[3]{x^2+3} ?
The first derivative of \sqrt[3]{x^2+3} is (2x)/(3(x^2+3)^{2/3)}