What is (\partial)/(\partial x)(z-x^2-y^2) ?

The answer to (\partial)/(\partial x)(z-x^2-y^2) is -2x

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(\partial)/(\partial x)(z-x^2-y^2)

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

- 2 x

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 - 2 x - 0

Simplify

= - 2 x

\int \frac{1}{8 + 3 x} d x

sin (5 x)

\frac{\partial}{\partial x} (x sin (2 y + x))

\frac{d}{d x} (\frac{x - 9}{7 x ^{2} e ^{x}})

\frac{d y}{d x} = \frac{1}{4} e^{x} - \frac{y}{x} + \frac{3 x}{4}

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