en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 2x*ln(x)

Solution

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

Solution

2 (ln (x) + 1)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = ln (x)

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

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

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

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

Simplify

2 (1 \cdot ln (x) + \frac{1}{x} x) : 2 (ln (x) + 1)

= 2 (ln (x) + 1)

Popular Examples

derivative of 4arctan(x)

\frac{d}{d x} (4 arctan (x))

x^2y^{''}-7xy^'+15y=0

x^{2} y^{^{''}} - 7 x y^{^{'}} + 15 y = 0

integral of 10xe^{0.1x^2}

\int 10 x e^{0.1 x^{2}} d x

(d^2y)/(dx^2)=-25y

\frac{d ^{2} y}{d x ^{2}} = - 25 y

laplacetransform (e^{2t}-e^1)/2 laplace transform

\frac{e ^{2 t} - e ^{1}}{2}

Frequently Asked Questions (FAQ)

What is the derivative of 2x*ln(x) ?
The derivative of 2x*ln(x) is 2(ln(x)+1)
What is the first derivative of 2x*ln(x) ?
The first derivative of 2x*ln(x) is 2(ln(x)+1)