What is the derivative of e^{sqrt(xy)} ?

The derivative of e^{sqrt(xy)} is (e^{sqrt(xy)}(y+x\frac{dy)/(dx))}{2sqrt(xy)}

What is the first derivative of e^{sqrt(xy)} ?

The first derivative of e^{sqrt(xy)} is (e^{sqrt(xy)}(y+x\frac{dy)/(dx))}{2sqrt(xy)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (e^{x y})

\frac{e ^{x y} ( y + x \frac{d y}{d x} )}{2 x y}

Solution steps

\frac{d}{d x} (e^{x y})

Apply the chain rule:

e^{x y} \frac{d}{d x} (x y)

= e^{x y} \frac{d}{d x} (x y)

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

= e^{x y} \frac{y + x \frac{d y}{d x}}{2 x y}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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