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

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

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

The first derivative of ln(sqrt((x^2-2/(x^2+2)))) is (4x)/((x^2+2)(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 (\frac{x ^{2} - 2}{x ^{2} + 2}))

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} - 2}{x ^{2} + 2}) = \frac{4 x}{x ^{2} - 2 ( x ^{2} + 2 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{x ^{2} - 2}{x ^{2} + 2}} \cdot \frac{4 x}{x ^{2} - 2 ( x ^{2} + 2 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{\frac{x ^{2} - 2}{x ^{2} + 2}} \cdot \frac{4 x}{x ^{2} - 2 ( x ^{2} + 2 ) ^{\frac{3}{2}}} : \frac{4 x}{( x ^{2} + 2 ) ( x ^{2} - 2 )}

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

\frac{d}{d x} (- 5 x^{\frac{4}{5}} + 3 x^{\frac{2}{3}} + 2)

\int_{- 9}^{9} 1 + (x)^{2} d x

x \to 9 lim (\frac{∣ x - 9 ∣}{x - 9})

\frac{\partial}{\partial x} (\frac{2 y}{3 x})

(x^{2} e^{x} + y) d x = x d y

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