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(x^2+4))

Solution

derivative of

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

Solution

\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}

Popular Examples

(3x+2y+1)*dx-(3x+2y-1)*dy=0

(3 x + 2 y + 1) \cdot d x - (3 x + 2 y - 1) \cdot d y = 0

integral of (2x^4+3x^3-x)/(x^3)

\int \frac{2 x ^{4} + 3 x ^{3} - x}{x ^{3}} d x

tangent of f(x)=sqrt(x+7),\at x=-6 tangent of

f (x) = x + 7, at x = - 6

derivative of 4^{-x/4}

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

derivative of (4x^2-3)/(8x^3+1)derivative of

\frac{4 x ^{2} - 3}{8 x ^{3} + 1}

Frequently Asked Questions (FAQ)

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))