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^2-4x+1)

Solution

derivative of

ln (x^{2} - 4 x + 1)

Solution

\frac{2 x - 4}{x ^{2} - 4 x + 1}

Solution steps

\frac{d}{d x} (ln (x^{2} - 4 x + 1))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 x - 4}{x ^{2} - 4 x + 1}

Popular Examples

(\partial)/(\partial y)(x*y^2)

\frac{\partial}{\partial y} (x \cdot y^{2})

implicit (dy)/(dx),y^3-2xy+7=3x+1 implicit derivative

\frac{d y}{d x}, y^{3} - 2 x y + 7 = 3 x + 1

limit as x approaches 0 of ((\sqrt[3]{x+8}-2))/x

integral of 5x*cos(8x)

\int 5 x \cdot cos (8 x) d x

derivative of-sin^2(x)

\frac{d}{d x} (- sin^{2} (x))

Frequently Asked Questions (FAQ)

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