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(4+x^2))

Solution

\frac{d}{d x} (ln (x + 4 + x^{2}))

Solution

\frac{1}{4 + x ^{2}}

Solution steps

\frac{d}{d x} (ln (x + 4 + x^{2}))

Apply the chain rule:

\frac{1}{x + 4 + x ^{2}} \frac{d}{d x} (x + 4 + x^{2})

= \frac{1}{x + 4 + x ^{2}} \frac{d}{d x} (x + 4 + x^{2})

\frac{d}{d x} (x + 4 + x^{2}) = 1 + \frac{x}{4 + x ^{2}}

= \frac{1}{x + 4 + x ^{2}} (1 + \frac{x}{4 + x ^{2}})

Simplify

\frac{1}{x + 4 + x ^{2}} (1 + \frac{x}{4 + x ^{2}}) : \frac{1}{4 + x ^{2}}

= \frac{1}{4 + x ^{2}}

Popular Examples

(\partial)/(\partial x)(e^xln(xy))

\frac{\partial}{\partial x} (e^{x} ln (x y))

derivative of 2x^3-3x^2-12+8 derivative of

2 x^{3} - 3 x^{2} - 12 + 8

sum from n=1 to infinity of 7^nx^{n-1}

n = 1 \sum \infty 7^{n} x^{n - 1}

y^{''}+6y^'+8y=cos(3t),y(0)=-2,y^'(0)=1

y^{^{''}} + 6 y^{^{'}} + 8 y = cos (3 t), y (0) = - 2, y^{^{'}} (0) = 1

integral from 6 to 8 of (86)/((x-6)^3)

\int_{6}^{8} \frac{86}{( x - 6 ) ^{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(4+x^2)) ?
The derivative of ln(x+sqrt(4+x^2)) is 1/(sqrt(4+x^2))
What is the first derivative of ln(x+sqrt(4+x^2)) ?
The first derivative of ln(x+sqrt(4+x^2)) is 1/(sqrt(4+x^2))