en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x+ye^y)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + y, g = e^{y}

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

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

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

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

Popular Examples

limit as x approaches-1/2 of 4x(3x+4)^2

x \to - \frac{1}{2} lim (4 x (3 x + 4)^{2})

limit as a approaches t of a^5+a^5

a \to t lim (a^{5} + a^{5})

(\partial)/(\partial z)(xy^2arctan(z))

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

integral from 1 to 2 of 3/(x^2)

\int_{1}^{2} \frac{3}{x ^{2}} d x

(\partial)/(\partial x)(xsqrt(xy))

\frac{\partial}{\partial x} (x x y)

Frequently Asked Questions (FAQ)

What is the derivative of (x+ye^y) ?
The derivative of (x+ye^y) is (1+(dy)/(dx))e^y+e^y(dy)/(dx)(x+y)
What is the first derivative of (x+ye^y) ?
The first derivative of (x+ye^y) is (1+(dy)/(dx))e^y+e^y(dy)/(dx)(x+y)