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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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