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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{1 + 5 t}{ln ( t ^{2} )}

\int \frac{x ^{2}}{x ^{6} - 1} d x

\int_{1}^{10} 5 x^{- 2} d x

\frac{d}{d x} (2 x^{3} - 5 x^{2} + 3 x - 1)

\frac{1}{s ( s ^{2} + 100 s + 10000 )}

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