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

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

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(\partial)/(\partial y)(ln(x^3+y^3))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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