What is the derivative of e^{x+ln(x}) ?

The derivative of e^{x+ln(x}) is e^xx+e^x

What is the first derivative of e^{x+ln(x}) ?

The first derivative of e^{x+ln(x}) is e^xx+e^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (e^{x + l n (x)})

e^{x} x + e^{x}

Solution steps

\frac{d}{d x} (e^{x + l n (x)})

Simplify

e^{x + l n (x)} : e^{x} x

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

Apply the Product Rule:

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

f = e^{x}, g = x

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

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

\frac{d x}{d x} = 1

= e^{x} x + 1 \cdot e^{x}

Simplify

= e^{x} x + e^{x}

x \to \infty lim ((- 2)^{x})

\frac{\partial}{\partial x} (2 π x y + π x^{2})

\frac{\partial}{\partial x} (e^{- 3 x})

cos (y) + (1 + e^{- x}) sin (y) \frac{d y}{d x} = 0

\int \frac{1}{5 x + 4} d x

What is the derivative of e^{x+ln(x}) ?
The derivative of e^{x+ln(x}) is e^xx+e^x
What is the first derivative of e^{x+ln(x}) ?
The first derivative of e^{x+ln(x}) is e^xx+e^x