en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (ln(x+3x)^2)

Solution

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

Solution

\frac{2 ln ( x )}{x} + 6 ln (x) + 6 + 18 x

Solution steps

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

Apply the chain rule:

2 (ln (x) + 3 x) \frac{d}{d x} (ln (x) + 3 x)

= 2 (ln (x) + 3 x) \frac{d}{d x} (ln (x) + 3 x)

\frac{d}{d x} (ln (x) + 3 x) = \frac{1}{x} + 3

= 2 (ln (x) + 3 x) (\frac{1}{x} + 3)

Simplify

2 (ln (x) + 3 x) (\frac{1}{x} + 3) : \frac{2 ln ( x )}{x} + 6 ln (x) + 6 + 18 x

= \frac{2 ln ( x )}{x} + 6 ln (x) + 6 + 18 x

Graph

Popular Examples

(\partial)/(\partial x)(ln(x+9y+2z))

\frac{\partial}{\partial x} (ln (x + 9 y + 2 z))

derivative of 2tan(x+pi/(12))

\frac{d}{d x} (2 tan (x + \frac{π}{12}))

derivative of (x+1^{2/3}(3x^2-2)^3)

\frac{d}{d x} ((x + 1)^{\frac{2}{3}} (3 x^{2} - 2)^{3})

integral of (sec(2x)tan(2x))

\int (sec (2 x) tan (2 x)) d x

integral of (m^3)/((z^2)^3)

\int \frac{m ^{3}}{( z ^{2} ) ^{3}} d m

Frequently Asked Questions (FAQ)

What is the derivative of (ln(x+3x)^2) ?
The derivative of (ln(x+3x)^2) is (2ln(x))/x+6ln(x)+6+18x
What is the first derivative of (ln(x+3x)^2) ?
The first derivative of (ln(x+3x)^2) is (2ln(x))/x+6ln(x)+6+18x