What is the derivative of ln(sqrt(x^2+19)) ?

The derivative of ln(sqrt(x^2+19)) is x/(x^2+19)

What is the first derivative of ln(sqrt(x^2+19)) ?

The first derivative of ln(sqrt(x^2+19)) is x/(x^2+19)

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\frac{d}{d x} (ln (x^{2} + 19))

\frac{x}{x ^{2} + 19}

Solution steps

\frac{d}{d x} (ln (x^{2} + 19))

Apply the chain rule:

\frac{1}{x ^{2} + 19} \frac{d}{d x} (x^{2} + 19)

= \frac{1}{x ^{2} + 19} \frac{d}{d x} (x^{2} + 19)

\frac{d}{d x} (x^{2} + 19) = \frac{x}{x ^{2} + 19}

= \frac{1}{x ^{2} + 19} \cdot \frac{x}{x ^{2} + 19}

Simplify

\frac{1}{x ^{2} + 19} \cdot \frac{x}{x ^{2} + 19} : \frac{x}{x ^{2} + 19}

= \frac{x}{x ^{2} + 19}

\int \frac{3}{6 x - x ^{2}} d x

f (x) = 5 x + 6, at a = 2

\frac{d}{d x} (ln (x^{2} - 14 x))

2 x^{2} - 80 x + y^{2} + 49 = 0 (0)

\int_{1}^{2} 4 - x^{2} d x

What is the derivative of ln(sqrt(x^2+19)) ?
The derivative of ln(sqrt(x^2+19)) is x/(x^2+19)
What is the first derivative of ln(sqrt(x^2+19)) ?
The first derivative of ln(sqrt(x^2+19)) is x/(x^2+19)