What is the derivative of ln((2x+1(x^2-2))) ?

The derivative of ln((2x+1(x^2-2))) is (6x^2+2x-4)/((2x+1)(x^2-2))

What is the first derivative of ln((2x+1(x^2-2))) ?

The first derivative of ln((2x+1(x^2-2))) is (6x^2+2x-4)/((2x+1)(x^2-2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{6 x ^{2} + 2 x - 4}{( 2 x + 1 ) ( x ^{2} - 2 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((2 x + 1) (x^{2} - 2)) = 6 x^{2} + 2 x - 4

= \frac{1}{( 2 x + 1 ) ( x ^{2} - 2 )} (6 x^{2} + 2 x - 4)

Simplify

\frac{1}{( 2 x + 1 ) ( x ^{2} - 2 )} (6 x^{2} + 2 x - 4) : \frac{6 x ^{2} + 2 x - 4}{( 2 x + 1 ) ( x ^{2} - 2 )}

= \frac{6 x ^{2} + 2 x - 4}{( 2 x + 1 ) ( x ^{2} - 2 )}

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

x \frac{d y}{d x} + 2 y = 10 x^{2}

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

\int \frac{3 - 6 x ^{3} + 4 x ^{6}}{x ^{6}} d x

f (x) = \frac{( 6 ln ( x ) )}{x}

What is the derivative of ln((2x+1(x^2-2))) ?
The derivative of ln((2x+1(x^2-2))) is (6x^2+2x-4)/((2x+1)(x^2-2))
What is the first derivative of ln((2x+1(x^2-2))) ?
The first derivative of ln((2x+1(x^2-2))) is (6x^2+2x-4)/((2x+1)(x^2-2))