en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

inverse oflaplace ((s+6))/(s^2+6s+25)inverse laplace

\frac{( s + 6 )}{s ^{2} + 6 s + 25}

derivative of 0.001x^3+4x+1458 derivative of

0.001 x^{3} + 4 x + 1458

derivative of f(x)= 1/(sqrt(x^{17))}derivative of

f (x) = \frac{1}{x ^{17}}

5x^{''}+25x^'+340x=0

5 x^{^{''}} + 25 x^{^{'}} + 340 x = 0

inverse oflaplace 1/((s-1)(s^2+9))inverse laplace

\frac{1}{( s - 1 ) ( s ^{2} + 9 )}

Frequently Asked Questions (FAQ)

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