What is the derivative of ln|1+x-x^3| ?

The derivative of ln|1+x-x^3| is (-3x^2+1)/(1+x-x^3)

What is the first derivative of ln|1+x-x^3| ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

cos (X^{2})

\int \frac{1}{x 1 + x ^{n}} d x

\int sin (x) 1 - cos (x) d x

\frac{d}{d x} (5 x^{4} - 3 x^{2} + 7)

x \to \infty lim ((a)^{x})

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