en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(x+sqrt(5+x^2))

Solution

derivative of

ln (x + 5 + x^{2})

Solution

\frac{1}{5 + x ^{2}}

Solution steps

\frac{d}{d x} (ln (x + 5 + x^{2}))

Apply the chain rule:

\frac{1}{x + 5 + x ^{2}} \frac{d}{d x} (x + 5 + x^{2})

= \frac{1}{x + 5 + x ^{2}} \frac{d}{d x} (x + 5 + x^{2})

\frac{d}{d x} (x + 5 + x^{2}) = 1 + \frac{x}{5 + x ^{2}}

= \frac{1}{x + 5 + x ^{2}} (1 + \frac{x}{5 + x ^{2}})

Simplify

\frac{1}{x + 5 + x ^{2}} (1 + \frac{x}{5 + x ^{2}}) : \frac{1}{5 + x ^{2}}

= \frac{1}{5 + x ^{2}}

Popular Examples

derivative of (-4/x)

\frac{d}{d x} (\frac{- 4}{x})

derivative of x(7x+1)^{1/3}derivative of

x (7 x + 1)^{\frac{1}{3}}

tangent of 5x^3-5x tangent of

5 x^{3} - 5 x

derivative of f(x)=sqrt((x^2)/3)derivative of

f (x) = \frac{x ^{2}}{3}

integral of ((arctan(x)))/(x^2)

\int \frac{( arctan ( x ) )}{x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(5+x^2)) ?
The derivative of ln(x+sqrt(5+x^2)) is 1/(sqrt(5+x^2))
What is the first derivative of ln(x+sqrt(5+x^2)) ?
The first derivative of ln(x+sqrt(5+x^2)) is 1/(sqrt(5+x^2))