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

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

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

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

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derivative of

f (x) = ln (x + 1 + x^{2})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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