What is the derivative of (sqrt(x)-2/x)^3 ?

The derivative of (sqrt(x)-2/x)^3 is (3(xsqrt(x)-2)^2(x^{3/2}+4))/(2x^{7/2)sqrt(x)}

What is the first derivative of (sqrt(x)-2/x)^3 ?

The first derivative of (sqrt(x)-2/x)^3 is (3(xsqrt(x)-2)^2(x^{3/2}+4))/(2x^{7/2)sqrt(x)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{3 ( x x - 2 ) ^{2} ( x ^{\frac{3}{2}} + 4 )}{2 x ^{\frac{7}{2}} x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (x - \frac{2}{x})^{2} \frac{x ^{\frac{3}{2}} + 4}{2 x ^{\frac{3}{2}} x} : \frac{3 ( x x - 2 ) ^{2} ( x ^{\frac{3}{2}} + 4 )}{2 x ^{\frac{7}{2}} x}

= \frac{3 ( x x - 2 ) ^{2} ( x ^{\frac{3}{2}} + 4 )}{2 x ^{\frac{7}{2}} x}

\int_{0}^{7} e^{x} - 7 d x

\frac{\partial}{\partial x} (z^{2} (sin (2 x y)))

y^{^{'}} = y (x y^{3} + 3)

\int_{0}^{3} \frac{x}{x ^{2} + 6 x + 13} d x

3 y^{^{''}} - 5 y^{^{'}} - 2 y = t^{3} - 2 t

What is the derivative of (sqrt(x)-2/x)^3 ?
The derivative of (sqrt(x)-2/x)^3 is (3(xsqrt(x)-2)^2(x^{3/2}+4))/(2x^{7/2)sqrt(x)}
What is the first derivative of (sqrt(x)-2/x)^3 ?
The first derivative of (sqrt(x)-2/x)^3 is (3(xsqrt(x)-2)^2(x^{3/2}+4))/(2x^{7/2)sqrt(x)}