en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(4x-x^2-3)

Solution

derivative of

ln (4 x - x^{2} - 3)

Solution

\frac{- 2 x + 4}{4 x - x ^{2} - 3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{- 2 x + 4}{4 x - x ^{2} - 3}

Popular Examples

integral of sin(2x)sin(cos(2x))

\int sin (2 x) sin (cos (2 x)) d x

(\partial)/(\partial x)(sin(3x+4y))

\frac{\partial}{\partial x} (sin (3 x + 4 y))

derivative of (4x+7)^2 derivative of

(4 x + 7)^{2}

integral of 1/(sqrt(2-x^2))

\int \frac{1}{2 - x ^{2}} d x

derivative of (sqrt(x+4)/(sqrt(x-1)))

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

Frequently Asked Questions (FAQ)

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