en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(3+x-x^3)

Solution

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

Solution

\frac{- 3 x ^{2} + 1}{3 + x - x ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of xsqrt(x-6)

\int x x - 6 d x

derivative of xsinh(x-8cosh(x))

\frac{d}{d x} (x sinh (x) - 8 cosh (x))

derivative of (x^2+3/(x-1))

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

integral of 5/(3x^2-2)

\int \frac{5}{3 x ^{2} - 2} d x

limit as x approaches infinity of-5^x

x \to \infty lim (- 5^{x})

Frequently Asked Questions (FAQ)

What is the derivative of ln(3+x-x^3) ?
The derivative of ln(3+x-x^3) is (-3x^2+1)/(3+x-x^3)
What is the first derivative of ln(3+x-x^3) ?
The first derivative of ln(3+x-x^3) is (-3x^2+1)/(3+x-x^3)