What is (\partial)/(\partial x)((x^2+y^2+z^2)^{0.5}) ?

The answer to (\partial)/(\partial x)((x^2+y^2+z^2)^{0.5}) is x/((x^2+y^2+z^2)^{1/2)}

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(\partial)/(\partial x)((x^2+y^2+z^2)^{0.5})

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{0.5})

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

Solution steps

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{0.5})

Treat

y, z

as constants

Apply the chain rule:

\frac{0.5}{( x ^{2} + y ^{2} + z ^{2} ) ^{0.5}} \frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2})

= \frac{0.5}{( x ^{2} + y ^{2} + z ^{2} ) ^{0.5}} \frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2})

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

= \frac{0.5}{( x ^{2} + y ^{2} + z ^{2} ) ^{0.5}} \cdot 2 x

Simplify

\frac{0.5}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{1}{2}}} \cdot 2 x : \frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{1}{2}}}

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

\int \frac{4 - x}{x ^{4} - x ^{2}} d x

x \to 2 lim (2 x + c)

f (x) = \frac{1 - ln ( x )}{2 x ^{2}}

\frac{d y}{d x} = ∣ x - 2 ∣

f (x) = (x^{2} - 4)^{2}

What is (\partial)/(\partial x)((x^2+y^2+z^2)^{0.5}) ?
The answer to (\partial)/(\partial x)((x^2+y^2+z^2)^{0.5}) is x/((x^2+y^2+z^2)^{1/2)}