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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\frac{\partial}{\partial x} (((1 x, 3 y, 4 z)) \cdot (1, 2, 3))

\int sin^{3} (x co) s^{12} x d x

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 1

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