en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^2log_{e}(2x)

Solution

\frac{d}{d x} (x^{2} lo g_{e} (2 x))

Solution

2 x ln (2 x) + x

Solution steps

\frac{d}{d x} (x^{2} lo g_{e} (2 x))

Simplify

x^{2} lo g_{e} (2 x) : x^{2} ln (2 x)

= \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)

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

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

= 2 x ln (2 x) + x

Popular Examples

(dy)/(dx)+4tan(4x)y=3cos(4x)

\frac{d y}{d x} + 4 tan (4 x) y = 3 cos (4 x)

slope of (0,1),(4,-5)slope

(0, 1), (4, - 5)

derivative of (1+x^2)/((1-x^2)^2)derivative of

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

derivative of ln(4-x)

\frac{d}{d x} (ln (4 - x))

derivative of (2-x/(x+4))

\frac{d}{d x} (\frac{2 - x}{x + 4})

Frequently Asked Questions (FAQ)

What is the derivative of x^2log_{e}(2x) ?
The derivative of x^2log_{e}(2x) is 2xln(2x)+x
What is the first derivative of x^2log_{e}(2x) ?
The first derivative of x^2log_{e}(2x) is 2xln(2x)+x