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

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

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(\partial)/(\partial x)(sqrt(x^2+y^2+z))

\frac{\partial}{\partial x} (x^{2} + y^{2} + z)

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

Solution steps

\frac{\partial}{\partial x} (x^{2} + y^{2} + z)

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = x (x^{4} - x^{3})

y = \frac{36 x}{x ^{2} + 36}, (- 3, - \frac{12}{5})

\frac{d}{d x} (21 x + x^{2})

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

\frac{\partial}{\partial x} (6 x + y^{3})

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