What is (\partial)/(\partial y)(sqrt(3x^2+4y^2)) ?

The answer to (\partial)/(\partial y)(sqrt(3x^2+4y^2)) is (4y)/(sqrt(3x^2+4y^2))

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(\partial)/(\partial y)(sqrt(3x^2+4y^2))

\frac{\partial}{\partial y} (3 x^{2} + 4 y^{2})

\frac{4 y}{3 x ^{2} + 4 y ^{2}}

Solution steps

\frac{\partial}{\partial y} (3 x^{2} + 4 y^{2})

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 3 x ^{2} + 4 y ^{2}} \frac{\partial}{\partial y} (3 x^{2} + 4 y^{2})

= \frac{1}{2 3 x ^{2} + 4 y ^{2}} \frac{\partial}{\partial y} (3 x^{2} + 4 y^{2})

\frac{\partial}{\partial y} (3 x^{2} + 4 y^{2}) = 8 y

= \frac{1}{2 3 x ^{2} + 4 y ^{2}} \cdot 8 y

Simplify

\frac{1}{2 3 x ^{2} + 4 y ^{2}} \cdot 8 y : \frac{4 y}{3 x ^{2} + 4 y ^{2}}

= \frac{4 y}{3 x ^{2} + 4 y ^{2}}

x \to 0 lim (1 + cos^{3} (x))

y^{^{'}} \cdot 1 + x^{2} = x y^{2}

\frac{d}{d x} (7 + 5 x)

f (x) = \frac{1}{x + 4}

{\frac{4 s}{4 s ^{2} + 1}}

What is (\partial)/(\partial y)(sqrt(3x^2+4y^2)) ?
The answer to (\partial)/(\partial y)(sqrt(3x^2+4y^2)) is (4y)/(sqrt(3x^2+4y^2))