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)

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

\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}}

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)