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

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

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(\partial)/(\partial y)(ln(x^6+y^7))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x ^{6} + y ^{7}} \frac{\partial}{\partial y} (x^{6} + y^{7})

= \frac{1}{x ^{6} + y ^{7}} \frac{\partial}{\partial y} (x^{6} + y^{7})

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

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

Simplify

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

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

x \to 6 - lim (cos (\frac{1}{x - 6}))

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

\frac{d}{d x} (\frac{10}{( 1 - x ) ^{3}})

\int (- \frac{6}{x ^{4}}) d x

\int \frac{2 x - 3}{( x ^{2} + 2 x - 3 ) ^{\frac{3}{2}}} d x

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