What is the derivative of ln(x^3-2x^2) ?

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

What is the first derivative of ln(x^3-2x^2) ?

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

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^{3} - 2 x^{2}))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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