What is the derivative of ln(x+sqrt(x^2+3)) ?

The derivative of ln(x+sqrt(x^2+3)) is 1/(sqrt(x^2+3))

What is the first derivative of ln(x+sqrt(x^2+3)) ?

The first derivative of ln(x+sqrt(x^2+3)) is 1/(sqrt(x^2+3))

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\frac{d}{d x} (ln (x + x^{2} + 3))

\frac{1}{x ^{2} + 3}

Solution steps

\frac{d}{d x} (ln (x + x^{2} + 3))

Apply the chain rule:

\frac{1}{x + x ^{2} + 3} \frac{d}{d x} (x + x^{2} + 3)

= \frac{1}{x + x ^{2} + 3} \frac{d}{d x} (x + x^{2} + 3)

\frac{d}{d x} (x + x^{2} + 3) = 1 + \frac{x}{x ^{2} + 3}

= \frac{1}{x + x ^{2} + 3} (1 + \frac{x}{x ^{2} + 3})

Simplify

\frac{1}{x + x ^{2} + 3} (1 + \frac{x}{x ^{2} + 3}) : \frac{1}{x ^{2} + 3}

= \frac{1}{x ^{2} + 3}

2 x (1 + y) d x - y d y = 0

x^{8} ln (x)

f (x) = e^{3 x}

f (x) = 3^{x l n (x)}

e^{4 t} sin (2 t)

What is the derivative of ln(x+sqrt(x^2+3)) ?
The derivative of ln(x+sqrt(x^2+3)) is 1/(sqrt(x^2+3))
What is the first derivative of ln(x+sqrt(x^2+3)) ?
The first derivative of ln(x+sqrt(x^2+3)) is 1/(sqrt(x^2+3))