What is the derivative of ln(x+sqrt(x^2+4)) ?

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

What is the first derivative of ln(x+sqrt(x^2+4)) ?

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

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derivative of

ln (x + x^{2} + 4)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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