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

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

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

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

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derivative of

ln (\frac{∣ x ∣}{1 + x ^{2}})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (4 x^{2} + 5 x y^{2})

\int (1 - 2 x) d x

f (x) = 2 x - 8, [7, 10]

\frac{d}{d t} (- 2 a sin (2 t) + 2 b cos (2 t))

n = 0 \sum \infty 3 n

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