What is the derivative of ln((x+1/(x^3+1))) ?

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(- 16 x^{2} + 36)^{2}

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

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

\int cos (- 3 x) d x

x y^{3} + 5 x y = 36, (6, 1)

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