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)=2x^2ln(2x)

Solution

derivative of

f (x) = 2 x^{2} ln (2 x)

Solution

2 (2 x ln (2 x) + x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

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

= 2 (2 x ln (2 x) + x)

Popular Examples

(\partial)/(\partial x)((ln(x^2+y^2))^{1/2})

\frac{\partial}{\partial x} ((ln (x^{2} + y^{2}))^{\frac{1}{2}})

integral of (x-2y)

\int (x - 2 y) d y

tangent of (18)/x tangent of

\frac{18}{x}

integral of t^{-4}

\int t^{- 4} d t

derivative of (x^2+x-2/(x^3+6))

\frac{d}{d x} (\frac{x ^{2} + x - 2}{x ^{3} + 6})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=2x^2ln(2x) ?
The derivative of f(x)=2x^2ln(2x) is 2(2xln(2x)+x)
What is the first derivative of f(x)=2x^2ln(2x) ?
The first derivative of f(x)=2x^2ln(2x) is 2(2xln(2x)+x)