What is (\partial)/(\partial x)(-1x^2-1y^2-3x+2y+1) ?

The answer to (\partial)/(\partial x)(-1x^2-1y^2-3x+2y+1) is -2x-3

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(\partial)/(\partial x)(-1x^2-1y^2-3x+2y+1)

\frac{\partial}{\partial x} (- 1 x^{2} - 1 y^{2} - 3 x + 2 y + 1)

- 2 x - 3

Solution steps

\frac{\partial}{\partial x} (- 1 \cdot x^{2} - 1 \cdot y^{2} - 3 x + 2 y + 1)

Simplify

- 1 \cdot x^{2} - 1 \cdot y^{2} - 3 x + 2 y + 1 : - x^{2} - y^{2} - 3 x + 2 y + 1

= \frac{\partial}{\partial x} (- x^{2} - y^{2} - 3 x + 2 y + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (2 y) + \frac{\partial}{\partial x} (1)

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

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

\frac{\partial}{\partial x} (3 x) = 3

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

\frac{\partial}{\partial x} (1) = 0

= - 2 x - 0 - 3 + 0 + 0

Simplify

= - 2 x - 3

\int 3 e^{7} d x

9 x^{2} + y = 9, x^{8} - y = 1

f (x) = 7 x - 2 x

\int \frac{1}{( x - 4 ) ^{5}} d x

f (x) = \frac{1}{x ^{2} + 2 x - 5}

What is (\partial)/(\partial x)(-1x^2-1y^2-3x+2y+1) ?
The answer to (\partial)/(\partial x)(-1x^2-1y^2-3x+2y+1) is -2x-3