What is (\partial)/(\partial x)(-5x^2-5y^2+xy) ?

The answer to (\partial)/(\partial x)(-5x^2-5y^2+xy) is y-10x

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(\partial)/(\partial x)(-5x^2-5y^2+xy)

\frac{\partial}{\partial x} (- 5 x^{2} - 5 y^{2} + x y)

y - 10 x

Solution steps

\frac{\partial}{\partial x} (- 5 x^{2} - 5 y^{2} + x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial x} (5 x^{2}) - \frac{\partial}{\partial x} (5 y^{2}) + \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

= - 10 x - 0 + y

Simplify

= y - 10 x

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

\frac{d}{d x} ((\frac{x + 9}{x - 9})^{5})

x \to - 6 - lim (\frac{x + 2}{x + 6})

\int \frac{9}{x ^{2} - 9 x} d x

\frac{x}{1 + x ^{2}}

What is (\partial)/(\partial x)(-5x^2-5y^2+xy) ?
The answer to (\partial)/(\partial x)(-5x^2-5y^2+xy) is y-10x