What is the derivative of ln(sqrt(x^4-4x)) ?

The derivative of ln(sqrt(x^4-4x)) is (2(x^3-1))/(x^4-4x)

What is the first derivative of ln(sqrt(x^4-4x)) ?

The first derivative of ln(sqrt(x^4-4x)) is (2(x^3-1))/(x^4-4x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{x ^{4} - 4 x} \frac{d}{d x} (x^{4} - 4 x)

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

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

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

Simplify

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

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

What is the derivative of ln(sqrt(x^4-4x)) ?
The derivative of ln(sqrt(x^4-4x)) is (2(x^3-1))/(x^4-4x)
What is the first derivative of ln(sqrt(x^4-4x)) ?
The first derivative of ln(sqrt(x^4-4x)) is (2(x^3-1))/(x^4-4x)