What is (\partial)/(\partial x)(ln(x^6+y^6)) ?

The answer to (\partial)/(\partial x)(ln(x^6+y^6)) is (6x^5)/(x^6+y^6)

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(\partial)/(\partial x)(ln(x^6+y^6))

\frac{\partial}{\partial x} (ln (x^{6} + y^{6}))

\frac{6 x ^{5}}{x ^{6} + y ^{6}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{6} + y^{6}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{6} + y ^{6}} \frac{\partial}{\partial x} (x^{6} + y^{6})

= \frac{1}{x ^{6} + y ^{6}} \frac{\partial}{\partial x} (x^{6} + y^{6})

\frac{\partial}{\partial x} (x^{6} + y^{6}) = 6 x^{5}

= \frac{1}{x ^{6} + y ^{6}} \cdot 6 x^{5}

Simplify

\frac{1}{x ^{6} + y ^{6}} \cdot 6 x^{5} : \frac{6 x ^{5}}{x ^{6} + y ^{6}}

= \frac{6 x ^{5}}{x ^{6} + y ^{6}}

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What is (\partial)/(\partial x)(ln(x^6+y^6)) ?
The answer to (\partial)/(\partial x)(ln(x^6+y^6)) is (6x^5)/(x^6+y^6)