What is (\partial)/(\partial x)(-5x^2-2xy-3y^2) ?

The answer to (\partial)/(\partial x)(-5x^2-2xy-3y^2) is -10x-2y

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(\partial)/(\partial x)(-5x^2-2xy-3y^2)

\frac{\partial}{\partial x} (- 5 x^{2} - 2 x y - 3 y^{2})

- 10 x - 2 y

Solution steps

\frac{\partial}{\partial x} (- 5 x^{2} - 2 x y - 3 y^{2})

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

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

\frac{\partial}{\partial x} (2 x y) = 2 y

\frac{\partial}{\partial x} (3 y^{2}) = 0

= - 10 x - 2 y - 0

Simplify

= - 10 x - 2 y

arccot (\frac{x}{9})

\int \frac{x - 1}{x + 1} d x

\int \frac{2 x + 3}{( x + 1 ) ^{2}} d x

8 x^{2} + 7 y^{2} = 56

\frac{d}{d x} (\frac{x ^{2}}{2 ( 1 - x )})

What is (\partial)/(\partial x)(-5x^2-2xy-3y^2) ?
The answer to (\partial)/(\partial x)(-5x^2-2xy-3y^2) is -10x-2y