What is (\partial)/(\partial y)(x/(x^6-y^4)) ?

The answer to (\partial)/(\partial y)(x/(x^6-y^4)) is (4xy^3)/((x^6-y^4)^2)

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(\partial)/(\partial y)(x/(x^6-y^4))

\frac{\partial}{\partial y} (\frac{x}{x ^{6} - y ^{4}})

\frac{4 x y ^{3}}{( x ^{6} - y ^{4} ) ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{x}{x ^{6} - y ^{4}})

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{\partial}{\partial y} (\frac{1}{x ^{6} - y ^{4}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= x \frac{\partial}{\partial y} ((x^{6} - y^{4})^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{6} - y ^{4} ) ^{2}} \frac{\partial}{\partial y} (x^{6} - y^{4})

= - \frac{1}{( x ^{6} - y ^{4} ) ^{2}} \frac{\partial}{\partial y} (x^{6} - y^{4})

\frac{\partial}{\partial y} (x^{6} - y^{4}) = - 4 y^{3}

= x (- \frac{1}{( x ^{6} - y ^{4} ) ^{2}} (- 4 y^{3}))

Simplify

x (- \frac{1}{( x ^{6} - y ^{4} ) ^{2}} (- 4 y^{3})) : \frac{4 x y ^{3}}{( x ^{6} - y ^{4} ) ^{2}}

= \frac{4 x y ^{3}}{( x ^{6} - y ^{4} ) ^{2}}

What is (\partial)/(\partial y)(x/(x^6-y^4)) ?
The answer to (\partial)/(\partial y)(x/(x^6-y^4)) is (4xy^3)/((x^6-y^4)^2)