What is (\partial)/(\partial x)(y^2-x^2-10) ?

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

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(\partial)/(\partial x)(y^2-x^2-10)

\frac{\partial}{\partial x} (y^{2} - x^{2} - 10)

- 2 x

Solution steps

\frac{\partial}{\partial x} (y^{2} - x^{2} - 10)

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} (10)

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

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

\frac{\partial}{\partial x} (10) = 0

= 0 - 2 x - 0

Simplify

= - 2 x

\frac{t d y}{d t} = t^{3} + 23 t^{3} y

\frac{( 6 x ^{2} - 5 ) ( x ^{2} - 6 )}{x ^{2} + 4}

y^{^{''}} - \frac{2 3}{3} y^{^{'}} + \frac{2}{9} = 0

\int_{0}^{2} (2 x - 1)^{2} d x

\int sec (3 t) tan (3 t) d t

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