en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(x*e^{2x})

Solution

\frac{d}{d x} (ln (x) \cdot e^{2 x})

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = ln (x), g = e^{2 x}

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

\frac{1}{x} e^{2 x} = \frac{e ^{2 x}}{x}

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

Popular Examples

(\partial)/(\partial x)(x^2y+3y^2-y)

\frac{\partial}{\partial x} (x^{2} y + 3 y^{2} - y)

((e^{4x^2})/(x^2))^'

(\frac{e ^{4 x^{2}}}{x ^{2}})^{^{'}}

integral of ((7x^9-20x^6))/(x^3)

\int \frac{( 7 x ^{9} - 20 x ^{6} )}{x ^{3}} d x

integral of (tan(x)+1/(tan(x)))^2

\int (tan (x) + \frac{1}{tan ( x )})^{2} d x

x^2y^{''}-2y=sin(ln(x))

x^{2} y^{^{''}} - 2 y = sin (ln (x))

Frequently Asked Questions (FAQ)

What is the derivative of ln(x*e^{2x}) ?
The derivative of ln(x*e^{2x}) is (e^{2x})/x+2e^{2x}ln(x)
What is the first derivative of ln(x*e^{2x}) ?
The first derivative of ln(x*e^{2x}) is (e^{2x})/x+2e^{2x}ln(x)