en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=sqrt(x^2+6x+1)

Solution

derivative of

f (x) = x^{2} + 6 x + 1

Solution

\frac{x + 3}{x ^{2} + 6 x + 1}

Solution steps

\frac{d}{d x} (x^{2} + 6 x + 1)

Apply the chain rule:

\frac{1}{2 x ^{2} + 6 x + 1} \frac{d}{d x} (x^{2} + 6 x + 1)

= \frac{1}{2 x ^{2} + 6 x + 1} \frac{d}{d x} (x^{2} + 6 x + 1)

\frac{d}{d x} (x^{2} + 6 x + 1) = 2 x + 6

= \frac{1}{2 x ^{2} + 6 x + 1} (2 x + 6)

Simplify

\frac{1}{2 x ^{2} + 6 x + 1} (2 x + 6) : \frac{x + 3}{x ^{2} + 6 x + 1}

= \frac{x + 3}{x ^{2} + 6 x + 1}

Popular Examples

derivative of y=(x^2+e^x)sqrt(x)derivative of

y = (x^{2} + e^{x}) x

d/(dy)(xsin(y))

\frac{d}{d y} (x sin (y))

limit as x approaches infinity of 5/4

x \to \infty lim (\frac{5}{4})

derivative of Ine^x

\frac{d}{d x} (I n e^{x})

integral of (x^{17}+3e^x-cos(x)+1/x)

\int (x^{17} + 3 e^{x} - cos (x) + \frac{1}{x}) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x^2+6x+1) ?
The derivative of f(x)=sqrt(x^2+6x+1) is (x+3)/(sqrt(x^2+6x+1))
What is the first derivative of f(x)=sqrt(x^2+6x+1) ?
The first derivative of f(x)=sqrt(x^2+6x+1) is (x+3)/(sqrt(x^2+6x+1))