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

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

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

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

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derivative of

y = x^{2} + 2

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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