en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sqrt(x)+1/(sqrt(x))

Solution

derivative of

x + \frac{1}{x}

Solution

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

Solution steps

\frac{d}{d x} (x + \frac{1}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{1}{2 x} - \frac{1}{2 x ^{\frac{3}{2}}}

Popular Examples

(\partial)/(\partial x)(5x^4+2xy^2+1)

\frac{\partial}{\partial x} (5 x^{4} + 2 x y^{2} + 1)

d/(dy)((1/(y^2)-5/(y^4))(y+7y^3))

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 7 y^{3}))

area x^2-3x,2x+6 area

x^{2} - 3 x, 2 x + 6

(\partial)/(\partial z)(x^2y-3xz+5y+7z)

\frac{\partial}{\partial z} (x^{2} y - 3 x z + 5 y + 7 z)

derivative of 20sin(x)

\frac{d}{d x} (20 sin (x))

Frequently Asked Questions (FAQ)

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