en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

derivative of

y = 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}}}

Graph

Popular Examples

(\partial)/(\partial x)(xy-2x^2y)

\frac{\partial}{\partial x} (x y - 2 x^{2} y)

y^'+y=e^{-4t}cos(3t),y(0)=0

y^{^{'}} + y = e^{- 4 t} cos (3 t), y (0) = 0

x^{2} y^{^{'}} + x y = 3

laplacetransform e^{-2t+3}laplace transform

e^{- 2 t + 3}

integral of 4/(θ^2)cos(4/θ)

\int \frac{4}{θ ^{2}} cos (\frac{4}{θ}) d θ

Frequently Asked Questions (FAQ)

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