What is the derivative of ln((x^2+1^3)) ?

The derivative of ln((x^2+1^3)) is (6x)/(x^2+1)

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

The first derivative of ln((x^2+1^3)) is (6x)/(x^2+1)

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

\frac{6 x}{x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{2} + 1)^{3}) = 6 x (x^{2} + 1)^{2}

= \frac{1}{( x ^{2} + 1 ) ^{3}} \cdot 6 x (x^{2} + 1)^{2}

Simplify

\frac{1}{( x ^{2} + 1 ) ^{3}} \cdot 6 x (x^{2} + 1)^{2} : \frac{6 x}{x ^{2} + 1}

= \frac{6 x}{x ^{2} + 1}

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

ln (15)

x \to 9 lim (ln (x - 9))

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

x^{2}, 4, [0, 2]

What is the derivative of ln((x^2+1^3)) ?
The derivative of ln((x^2+1^3)) is (6x)/(x^2+1)
What is the first derivative of ln((x^2+1^3)) ?
The first derivative of ln((x^2+1^3)) is (6x)/(x^2+1)