What is (\partial)/(\partial x)(sqrt(x^2+1)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+1)) is x/(sqrt(x^2+1))

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(\partial)/(\partial x)(sqrt(x^2+1))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 2 x e^{x} cos (x), at x = 0

\int_{0}^{2} sin (x) + e^{x} d x

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

s^{2} - 4 s + 3

\int (x^{4} - 1) x^{2} d x

What is (\partial)/(\partial x)(sqrt(x^2+1)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+1)) is x/(sqrt(x^2+1))