What is (\partial)/(\partial x)(y^2-x^2-8) ?

The answer to (\partial)/(\partial x)(y^2-x^2-8) is -2x

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(\partial)/(\partial x)(y^2-x^2-8)

\frac{\partial}{\partial x} (y^{2} - x^{2} - 8)

- 2 x

Solution steps

\frac{\partial}{\partial x} (y^{2} - x^{2} - 8)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (8)

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

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

\frac{\partial}{\partial x} (8) = 0

= 0 - 2 x - 0

Simplify

= - 2 x

\int \frac{1}{x ^{\frac{8}{9}} ( 5 + x ^{\frac{1}{9}} )} d x

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

2 x lo g_{4} (x)

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

\int \frac{2}{3} e^{3 x} x d x

What is (\partial)/(\partial x)(y^2-x^2-8) ?
The answer to (\partial)/(\partial x)(y^2-x^2-8) is -2x