What is (\partial)/(\partial x)(sqrt(x^2+4)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+4)) is x/(sqrt(x^2+4))

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(\partial)/(\partial x)(sqrt(x^2+4))

\frac{\partial}{\partial x} (x^{2} + 4)

\frac{x}{x ^{2} + 4}

Solution steps

\frac{\partial}{\partial x} (x^{2} + 4)

Apply the chain rule:

\frac{1}{2 x ^{2} + 4} \frac{\partial}{\partial x} (x^{2} + 4)

= \frac{1}{2 x ^{2} + 4} \frac{\partial}{\partial x} (x^{2} + 4)

\frac{\partial}{\partial x} (x^{2} + 4) = 2 x

= \frac{1}{2 x ^{2} + 4} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} + 4} \cdot 2 x : \frac{x}{x ^{2} + 4}

= \frac{x}{x ^{2} + 4}

y = 8 x^{\frac{1}{2}} + 4 x^{\frac{3}{2}} + 4

x \to \infty lim (\frac{x - cos ( x )}{x})

\int \frac{- x}{( x + 1 ) - x + 1} d x

y = x^{2} - 8 x - 6

\frac{d y}{d x} = x e^{6 x - 5 y}

What is (\partial)/(\partial x)(sqrt(x^2+4)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+4)) is x/(sqrt(x^2+4))