en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(x+2sqrt(x))e^x

Solution

derivative of

f (x) = (x + 2 x) e^{x}

Solution

(1 + \frac{1}{x}) e^{x} + e^{x} (x + 2 x)

Solution steps

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

Apply the Product Rule:

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

f = x + 2 x, g = e^{x}

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

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

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

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

Popular Examples

integral of (13)/(13+e^x)

\int \frac{13}{13 + e ^{x}} d x

(dy)/(dx)=6-3x^2

\frac{d y}{d x} = 6 - 3 x^{2}

integral of e^x*x^{-1}

\int e^{x} \cdot x^{- 1} d x

(dy}{dx}=\frac{4sqrt(y)ln(x))/x

\frac{d y}{d x} = \frac{4 y ln ( x )}{x}

slope ofintercept (1.23)(2.46)slope intercept

(1.23) (2.46)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x+2sqrt(x))e^x ?
The derivative of f(x)=(x+2sqrt(x))e^x is (1+1/(sqrt(x)))e^x+e^x(x+2sqrt(x))
What is the first derivative of f(x)=(x+2sqrt(x))e^x ?
The first derivative of f(x)=(x+2sqrt(x))e^x is (1+1/(sqrt(x)))e^x+e^x(x+2sqrt(x))