What is (\partial)/(\partial x)(sqrt(x^2+8)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+8)) is x/(sqrt(x^2+8))

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(\partial)/(\partial x)(sqrt(x^2+8))

\frac{\partial}{\partial x} (x^{2} + 8)

\frac{x}{x ^{2} + 8}

Solution steps

\frac{\partial}{\partial x} (x^{2} + 8)

Apply the chain rule:

\frac{1}{2 x ^{2} + 8} \frac{\partial}{\partial x} (x^{2} + 8)

= \frac{1}{2 x ^{2} + 8} \frac{\partial}{\partial x} (x^{2} + 8)

\frac{\partial}{\partial x} (x^{2} + 8) = 2 x

= \frac{1}{2 x ^{2} + 8} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} + 8} \cdot 2 x : \frac{x}{x ^{2} + 8}

= \frac{x}{x ^{2} + 8}

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What is (\partial)/(\partial x)(sqrt(x^2+8)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+8)) is x/(sqrt(x^2+8))