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

The derivative of ln((x^2+1^2)) is (4x)/(x^2+1)

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

The first derivative of ln((x^2+1^2)) is (4x)/(x^2+1)

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

\frac{4 x}{x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 4 x (x^{2} + 1)

Simplify

\frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 4 x (x^{2} + 1) : \frac{4 x}{x ^{2} + 1}

= \frac{4 x}{x ^{2} + 1}

y = x^{2} - 5, (2, - 1)

\frac{\partial}{\partial x} (x \cdot ln (2 y))

x \to 0 lim (\frac{2 x}{ln ( x )})

4 x (x^{2} - 4)

What is the derivative of ln((x^2+1^2)) ?
The derivative of ln((x^2+1^2)) is (4x)/(x^2+1)
What is the first derivative of ln((x^2+1^2)) ?
The first derivative of ln((x^2+1^2)) is (4x)/(x^2+1)