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

The answer to (\partial)/(\partial y)(-6xy-x^6-y^6) is -6x-6y^5

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

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

- 6 x - 6 y^{5}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (6 x y) = 6 x

\frac{\partial}{\partial y} (x^{6}) = 0

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

= - 6 x - 0 - 6 y^{5}

Simplify

= - 6 x - 6 y^{5}

\frac{( 4 x + 3 ) ^{8}}{( x ) ^{4}}

x \to 0 lim (\frac{6}{1 + x})

\frac{\partial}{\partial x} (e^{5 x + 3 y})

\frac{d}{d y} (\frac{1}{t} + \frac{1}{t ^{2}} - \frac{y}{t ^{2} + y ^{2}})

f (x) = 1 - \frac{1}{x ^{2}}

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