What is the derivative of ln(sqrt(x^2+5)) ?

The derivative of ln(sqrt(x^2+5)) is x/(x^2+5)

What is the first derivative of ln(sqrt(x^2+5)) ?

The first derivative of ln(sqrt(x^2+5)) is x/(x^2+5)

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\frac{d}{d x} (ln (x^{2} + 5))

\frac{x}{x ^{2} + 5}

Solution steps

\frac{d}{d x} (ln (x^{2} + 5))

Apply the chain rule:

\frac{1}{x ^{2} + 5} \frac{d}{d x} (x^{2} + 5)

= \frac{1}{x ^{2} + 5} \frac{d}{d x} (x^{2} + 5)

\frac{d}{d x} (x^{2} + 5) = \frac{x}{x ^{2} + 5}

= \frac{1}{x ^{2} + 5} \cdot \frac{x}{x ^{2} + 5}

Simplify

\frac{1}{x ^{2} + 5} \cdot \frac{x}{x ^{2} + 5} : \frac{x}{x ^{2} + 5}

= \frac{x}{x ^{2} + 5}

\frac{d}{d x} ((5 + 3 x) sin (x))

(y^{4} x) (\frac{d y}{d x}) = 1 + x, y (1) = 15

\frac{d y}{d x} = 3 - 2 y

x \to 7 lim (\frac{6 + 3}{6 ( 6 )})

\int 4 e^{4 x} d x

What is the derivative of ln(sqrt(x^2+5)) ?
The derivative of ln(sqrt(x^2+5)) is x/(x^2+5)
What is the first derivative of ln(sqrt(x^2+5)) ?
The first derivative of ln(sqrt(x^2+5)) is x/(x^2+5)