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+y)

Solution

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

Solution

\frac{1 + \frac{d y}{d x}}{2 x + y}

Solution steps

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

Apply the chain rule:

\frac{1}{2 x + y} \frac{d}{d x} (x + y)

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

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

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

Simplify

\frac{1}{2 x + y} (1 + \frac{d y}{d x}) : \frac{1 + \frac{d y}{d x}}{2 x + y}

= \frac{1 + \frac{d y}{d x}}{2 x + y}

Popular Examples

taylor x-x^3,-2 taylor

x - x^{3}, - 2

(\partial)/(\partial y)(3xz^2e^{y^2})

\frac{\partial}{\partial y} (3 x z^{2} e^{y^{2}})

derivative of f(x)= 1/x+1/(x^2)+1/(x^3)derivative of

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

(tdy)/(dt)+(t+1)y=t

\frac{t d y}{d t} + (t + 1) y = t

derivative of y=be^{e^3+x^3}derivative of

y = b e^{e^{3} + x^{3}}

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x+y) ?
The derivative of sqrt(x+y) is (1+\frac{dy)/(dx)}{2sqrt(x+y)}
What is the first derivative of sqrt(x+y) ?
The first derivative of sqrt(x+y) is (1+\frac{dy)/(dx)}{2sqrt(x+y)}