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(9+x^2))

Solution

\frac{d}{d x} (ln (x + 9 + x^{2}))

Solution

\frac{1}{9 + x ^{2}}

Solution steps

\frac{d}{d x} (ln (x + 9 + x^{2}))

Apply the chain rule:

\frac{1}{x + 9 + x ^{2}} \frac{d}{d x} (x + 9 + x^{2})

= \frac{1}{x + 9 + x ^{2}} \frac{d}{d x} (x + 9 + x^{2})

\frac{d}{d x} (x + 9 + x^{2}) = 1 + \frac{x}{9 + x ^{2}}

= \frac{1}{x + 9 + x ^{2}} (1 + \frac{x}{9 + x ^{2}})

Simplify

\frac{1}{x + 9 + x ^{2}} (1 + \frac{x}{9 + x ^{2}}) : \frac{1}{9 + x ^{2}}

= \frac{1}{9 + x ^{2}}

Graph

Popular Examples

area 2x+1,x^2-4x area

2 x + 1, x^{2} - 4 x

(d^2)/(dx^2)((e^x)/(5+e^x))

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

f(x)=(x^3-2x^2+3x+1)^{11}

f (x) = (x^{3} - 2 x^{2} + 3 x + 1)^{11}

derivative of x-sqrt(1-x^2)

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

y^{''}+4y^'+8y=0

y^{^{''}} + 4 y^{^{'}} + 8 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(9+x^2)) ?
The derivative of ln(x+sqrt(9+x^2)) is 1/(sqrt(9+x^2))
What is the first derivative of ln(x+sqrt(9+x^2)) ?
The first derivative of ln(x+sqrt(9+x^2)) is 1/(sqrt(9+x^2))