What is (\partial)/(\partial x)(sqrt(x^2+5)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+5)) is x/(sqrt(x^2+5))

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(\partial)/(\partial x)(sqrt(x^2+5))

\frac{\partial}{\partial x} (x^{2} + 5)

\frac{x}{x ^{2} + 5}

Solution steps

\frac{\partial}{\partial x} (x^{2} + 5)

Apply the chain rule:

\frac{1}{2 x ^{2} + 5} \frac{\partial}{\partial x} (x^{2} + 5)

= \frac{1}{2 x ^{2} + 5} \frac{\partial}{\partial x} (x^{2} + 5)

\frac{\partial}{\partial x} (x^{2} + 5) = 2 x

= \frac{1}{2 x ^{2} + 5} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} + 5} \cdot 2 x : \frac{x}{x ^{2} + 5}

= \frac{x}{x ^{2} + 5}

\frac{5 x}{e ^{x}}

x^{2} y^{^{''}} - 4 x y^{^{'}} = x^{5}

f (x) = (3 x^{2} - x + 5) (x^{2} + 3 x - 9)

x \to 2 + lim (\frac{- 2}{x ^{2} - 4})

x \to 0 lim (- \frac{3}{x ^{2}})

What is (\partial)/(\partial x)(sqrt(x^2+5)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+5)) is x/(sqrt(x^2+5))