en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

Solution

derivative of

f (x) = x^{2} + 2 x + 3

Solution

\frac{x + 1}{x ^{2} + 2 x + 3}

Solution steps

\frac{d}{d x} (x^{2} + 2 x + 3)

Apply the chain rule:

\frac{1}{2 x ^{2} + 2 x + 3} \frac{d}{d x} (x^{2} + 2 x + 3)

= \frac{1}{2 x ^{2} + 2 x + 3} \frac{d}{d x} (x^{2} + 2 x + 3)

\frac{d}{d x} (x^{2} + 2 x + 3) = 2 x + 2

= \frac{1}{2 x ^{2} + 2 x + 3} (2 x + 2)

Simplify

\frac{1}{2 x ^{2} + 2 x + 3} (2 x + 2) : \frac{x + 1}{x ^{2} + 2 x + 3}

= \frac{x + 1}{x ^{2} + 2 x + 3}

Graph

Popular Examples

integral of 4 x/((x+2)^{(1/4))}

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

limit as x approaches 1-of 3^{1/x}

x \to 1 - lim (3^{\frac{1}{x}})

(x^2+4)y^'+3xy=x

(x^{2} + 4) y^{^{'}} + 3 x y = x

limit as x approaches 0 of (e^{ax}-1)/x

x \to 0 lim (\frac{e ^{a x} - 1}{x})

integral of (7/(x^3))

\int (\frac{7}{x ^{3}}) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x^2+2x+3) ?
The derivative of f(x)=sqrt(x^2+2x+3) is (x+1)/(sqrt(x^2+2x+3))
What is the first derivative of f(x)=sqrt(x^2+2x+3) ?
The first derivative of f(x)=sqrt(x^2+2x+3) is (x+1)/(sqrt(x^2+2x+3))