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(x-1))

Solution

\frac{d}{d x} (ln (x) (x - 1))

Solution

\frac{x - 1}{x} + ln (x)

Solution steps

\frac{d}{d x} (ln (x) (x - 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = x - 1

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

Simplify

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

= \frac{x - 1}{x} + ln (x)

Popular Examples

implicit (dy)/(dx),5cos(8x)sin(5y)=8 implicit derivative

\frac{d y}{d x}, 5 cos (8 x) sin (5 y) = 8

y^{^{''}} = 12 t - 2

derivative of (6x^2+3x+7)/(sqrt(x))derivative of

\frac{6 x ^{2} + 3 x + 7}{x}

y^'=0.0011y*(2900-y)

y^{^{'}} = 0.0011 y \cdot (2900 - y)

integral of 8e^{5x+e^{5x}}

\int 8 e^{5 x + e^{5 x}} d x

Frequently Asked Questions (FAQ)

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