en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (ln(x^2)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

\frac{d x}{d x} = 1

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

Simplify

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

= \frac{2 - 2 ln ( x )}{x ^{2}}

Popular Examples

(t^2+1)f^'(t)+[f(t)]^2+1=0

(t^{2} + 1) f^{^{'}} (t) + [f (t)]^{2} + 1 = 0

integral from 2 to 3 of 6/(sqrt(3-x))

\int_{2}^{3} \frac{6}{3 - x} d x

derivative of ((x+8/(x-8))^5)

\frac{d}{d x} ((\frac{x + 8}{x - 8})^{5})

integral from 2 to 5 of x^2-6x+9

\int_{2}^{5} x^{2} - 6 x + 9 d x

d/(da)(cos(3a)cos(2a)+sin(4a)sin(a))

\frac{d}{d a} (cos (3 a) cos (2 a) + sin (4 a) sin (a))

Frequently Asked Questions (FAQ)

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