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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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