What is the derivative of (4x/(3(x^2-4)^{1/3)}) ?

The derivative of (4x/(3(x^2-4)^{1/3)}) is (4(x^2-12))/(9(x^2-4)^{4/3)}

What is the first derivative of (4x/(3(x^2-4)^{1/3)}) ?

The first derivative of (4x/(3(x^2-4)^{1/3)}) is (4(x^2-12))/(9(x^2-4)^{4/3)}

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{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}})

\frac{4 ( x ^{2} - 12 )}{9 ( x ^{2} - 4 ) ^{\frac{4}{3}}}

Solution steps

\frac{d}{d x} (\frac{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{4}{3} \frac{d}{d x} (\frac{x}{( x ^{2} - 4 ) ^{\frac{1}{3}}})

Apply the Quotient Rule:

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

= \frac{4}{3} \cdot \frac{\frac{d x}{d x} ( x ^{2} - 4 ) ^{\frac{1}{3}} - \frac{d}{d x} ( ( x ^{2} - 4 ) ^{\frac{1}{3}} ) x}{( ( x ^{2} - 4 ) ^{\frac{1}{3}} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{2} - 4)^{\frac{1}{3}}) = \frac{2 x}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}}

= \frac{4}{3} \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{\frac{1}{3}} - \frac{2 x}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} x}{( ( x ^{2} - 4 ) ^{\frac{1}{3}} ) ^{2}}

Simplify

\frac{4}{3} \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{\frac{1}{3}} - \frac{2 x}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} x}{( ( x ^{2} - 4 ) ^{\frac{1}{3}} ) ^{2}} : \frac{4 ( x ^{2} - 12 )}{9 ( x ^{2} - 4 ) ^{\frac{4}{3}}}

= \frac{4 ( x ^{2} - 12 )}{9 ( x ^{2} - 4 ) ^{\frac{4}{3}}}

\frac{d}{d x} (\frac{sin ( x )}{2 cos ^{2} ( x )})

x \to 0 + lim (sin^{x} (x))

\int_{5}^{2} (\frac{12 - x ^{3}}{x ^{4}}) d x

(t^{4} - 1)^{9} (t^{3} + 1)^{8}

\frac{d}{d x} (\frac{2 tan ( x )}{1 - tan ^{2} ( x )})

What is the derivative of (4x/(3(x^2-4)^{1/3)}) ?
The derivative of (4x/(3(x^2-4)^{1/3)}) is (4(x^2-12))/(9(x^2-4)^{4/3)}
What is the first derivative of (4x/(3(x^2-4)^{1/3)}) ?
The first derivative of (4x/(3(x^2-4)^{1/3)}) is (4(x^2-12))/(9(x^2-4)^{4/3)}