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

The derivative of (\sqrt[3]{x}/(x^2+x)) is (x^{1/3}(x+1)-3\sqrt[3]{x}(2x+1))/(3(x^2+x)^2)

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

The first derivative of (\sqrt[3]{x}/(x^2+x)) is (x^{1/3}(x+1)-3\sqrt[3]{x}(2x+1))/(3(x^2+x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

f (x) = \frac{3}{x}, (1, 3)

y \to 0 lim (\frac{8}{y ^{2} + y} - \frac{8}{y})

y^{^{''}} + 3 y^{^{'}} - 10 y = x (e^{x} + 1)

\frac{d}{d x} (3^{- 6 x + 6})

f^{^{'}} (x) = 3 x^{2} (8 - x^{- 3})

What is the derivative of (\sqrt[3]{x}/(x^2+x)) ?
The derivative of (\sqrt[3]{x}/(x^2+x)) is (x^{1/3}(x+1)-3\sqrt[3]{x}(2x+1))/(3(x^2+x)^2)
What is the first derivative of (\sqrt[3]{x}/(x^2+x)) ?
The first derivative of (\sqrt[3]{x}/(x^2+x)) is (x^{1/3}(x+1)-3\sqrt[3]{x}(2x+1))/(3(x^2+x)^2)