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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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