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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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