What is the slope of sqrt(x)+1/(sqrt(x^3)) ?

The slope of sqrt(x)+1/(sqrt(x^3)) is 1/(2sqrt(x))-(3x^2)/(2(x^3)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

slope of sqrt(x)+1/(sqrt(x^3))

slope

x + \frac{1}{x ^{3}}

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

Solution steps

y = x + \frac{1}{x ^{3}}

In order to find the slope of the function, take the derivative of

x + \frac{1}{x ^{3}}

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

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

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

\int \frac{1}{( u + 1 ) ^{2}} d u

x^{2} y^{^{'}} = 1 - x^{2} + y^{2} - x^{2} y^{2}

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

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

What is the slope of sqrt(x)+1/(sqrt(x^3)) ?
The slope of sqrt(x)+1/(sqrt(x^3)) is 1/(2sqrt(x))-(3x^2)/(2(x^3)^{3/2)}