What is the derivative of ln(x+sqrt(7+x^2)) ?

The derivative of ln(x+sqrt(7+x^2)) is 1/(sqrt(7+x^2))

What is the first derivative of ln(x+sqrt(7+x^2)) ?

The first derivative of ln(x+sqrt(7+x^2)) is 1/(sqrt(7+x^2))

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\frac{d}{d x} (ln (x + 7 + x^{2}))

\frac{1}{7 + x ^{2}}

Solution steps

\frac{d}{d x} (ln (x + 7 + x^{2}))

Apply the chain rule:

\frac{1}{x + 7 + x ^{2}} \frac{d}{d x} (x + 7 + x^{2})

= \frac{1}{x + 7 + x ^{2}} \frac{d}{d x} (x + 7 + x^{2})

\frac{d}{d x} (x + 7 + x^{2}) = 1 + \frac{x}{7 + x ^{2}}

= \frac{1}{x + 7 + x ^{2}} (1 + \frac{x}{7 + x ^{2}})

Simplify

\frac{1}{x + 7 + x ^{2}} (1 + \frac{x}{7 + x ^{2}}) : \frac{1}{7 + x ^{2}}

= \frac{1}{7 + x ^{2}}

What is the derivative of ln(x+sqrt(7+x^2)) ?
The derivative of ln(x+sqrt(7+x^2)) is 1/(sqrt(7+x^2))
What is the first derivative of ln(x+sqrt(7+x^2)) ?
The first derivative of ln(x+sqrt(7+x^2)) is 1/(sqrt(7+x^2))