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

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

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

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

- 6 x^{5} - 6 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

= - 6 x^{5} - 6 y

\int \frac{1}{6 x + 5} d x

\int 3 x + 3 d x

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

\frac{d y}{d t} = 0.5 - t + 2 y

x \to 0 lim ((\frac{e}{x})^{x})

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