What is the derivative of sqrt(x-\sqrt{y)} ?

The derivative of sqrt(x-\sqrt{y)} is (2sqrt(y)-\frac{dy)/(dx)}{4sqrt(y)sqrt(x-\sqrt{y)}}

What is the first derivative of sqrt(x-\sqrt{y)} ?

The first derivative of sqrt(x-\sqrt{y)} is (2sqrt(y)-\frac{dy)/(dx)}{4sqrt(y)sqrt(x-\sqrt{y)}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{2 y - \frac{d y}{d x}}{4 y 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{\frac{d y}{d x}}{2 y}

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

Simplify

\frac{1}{2 x - y} (1 - \frac{\frac{d y}{d x}}{2 y}) : \frac{2 y - \frac{d y}{d x}}{4 y x - y}

= \frac{2 y - \frac{d y}{d x}}{4 y x - y}

e e^{2 x}

2.0219 \cdot 1 0^{- 4}

2 e^{x} \cdot e^{x + 3}

e^{- y} [- x (x + 2 y - 2)]

5000 e^{- 200}

What is the derivative of sqrt(x-\sqrt{y)} ?
The derivative of sqrt(x-\sqrt{y)} is (2sqrt(y)-\frac{dy)/(dx)}{4sqrt(y)sqrt(x-\sqrt{y)}}
What is the first derivative of sqrt(x-\sqrt{y)} ?
The first derivative of sqrt(x-\sqrt{y)} is (2sqrt(y)-\frac{dy)/(dx)}{4sqrt(y)sqrt(x-\sqrt{y)}}