What is (\partial)/(\partial y)(ln(x^7+y^7)) ?

The answer to (\partial)/(\partial y)(ln(x^7+y^7)) is (7y^6)/(x^7+y^7)

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(\partial)/(\partial y)(ln(x^7+y^7))

\frac{\partial}{\partial y} (ln (x^{7} + y^{7}))

\frac{7 y ^{6}}{x ^{7} + y ^{7}}

Solution steps

\frac{\partial}{\partial y} (ln (x^{7} + y^{7}))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x ^{7} + y ^{7}} \frac{\partial}{\partial y} (x^{7} + y^{7})

= \frac{1}{x ^{7} + y ^{7}} \frac{\partial}{\partial y} (x^{7} + y^{7})

\frac{\partial}{\partial y} (x^{7} + y^{7}) = 7 y^{6}

= \frac{1}{x ^{7} + y ^{7}} \cdot 7 y^{6}

Simplify

\frac{1}{x ^{7} + y ^{7}} \cdot 7 y^{6} : \frac{7 y ^{6}}{x ^{7} + y ^{7}}

= \frac{7 y ^{6}}{x ^{7} + y ^{7}}

\frac{( x - 3 ) ^{2}}{3}, 9 - x

\int θ - csc (θ) cot (θ) d θ

y \to 0 lim (\frac{2}{y ^{2} + y} - \frac{2}{y})

f (x) = 2^{l n (x)}

6 x^{2} - 9 x - 6, 7 x^{2} - 5 x - 3

What is (\partial)/(\partial y)(ln(x^7+y^7)) ?
The answer to (\partial)/(\partial y)(ln(x^7+y^7)) is (7y^6)/(x^7+y^7)