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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{4 x}{5 - tan ( x )}

\int 4 x (x^{2} - 3)^{5} d x

\frac{\partial}{\partial y} (20 - 5 x y - 5 x)

\frac{d}{d x} (2 lo g_{e} (x))

lo g_{2} (x)

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