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

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

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

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

Popular >

derivative of

ln (x^{2} + 1)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{x ^{2} + 1} \cdot \frac{x}{x ^{2} + 1} : \frac{x}{x ^{2} + 1}

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

\int \frac{1}{x ^{2} + x + 1} d x

\int \frac{9 + x + x ^{2}}{x} d x

(x^{2} + 3) (x^{3} + 5)

x \to \infty lim (x^{3} e^{x})

f (x) = 2 x^{2} + 8 x, at x = 4

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