What is (\partial)/(\partial x)(sqrt(3x^2+y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(3x^2+y^2)) is (3x)/(sqrt(3x^2+y^2))

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(\partial)/(\partial x)(sqrt(3x^2+y^2))

\frac{\partial}{\partial x} (3 x^{2} + y^{2})

\frac{3 x}{3 x ^{2} + y ^{2}}

Solution steps

\frac{\partial}{\partial x} (3 x^{2} + y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 3 x ^{2} + y ^{2}} \frac{\partial}{\partial x} (3 x^{2} + y^{2})

= \frac{1}{2 3 x ^{2} + y ^{2}} \frac{\partial}{\partial x} (3 x^{2} + y^{2})

\frac{\partial}{\partial x} (3 x^{2} + y^{2}) = 6 x

= \frac{1}{2 3 x ^{2} + y ^{2}} \cdot 6 x

Simplify

\frac{1}{2 3 x ^{2} + y ^{2}} \cdot 6 x : \frac{3 x}{3 x ^{2} + y ^{2}}

= \frac{3 x}{3 x ^{2} + y ^{2}}

What is (\partial)/(\partial x)(sqrt(3x^2+y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(3x^2+y^2)) is (3x)/(sqrt(3x^2+y^2))