What is the derivative of sqrt(x^2+2x+2) ?

The derivative of sqrt(x^2+2x+2) is (x+1)/(sqrt(x^2+2x+2))

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 2 lim (sin (2 x))

\int r^{2} - x^{2} d x

\frac{d y}{d x} + y = - 1

\frac{d y}{d x} = 6 - x

f (x) = 2 x^{2} - 10 x + 9, (2, - 3)

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