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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (6 x^{7})

\frac{d}{d x} (3 a x + b x^{3})

\frac{\partial}{\partial x} (3 x^{2} + 5 x y - 7 y^{2} + 1)

\frac{d}{d x} (e^{x^{2} + 4})

\int x^{2} (6 - x^{3}) d x

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