What is (\partial)/(\partial x)(45-x^2-y^2) ?

The answer to (\partial)/(\partial x)(45-x^2-y^2) is -2x

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(\partial)/(\partial x)(45-x^2-y^2)

\frac{\partial}{\partial x} (45 - x^{2} - y^{2})

- 2 x

Solution steps

\frac{\partial}{\partial x} (45 - x^{2} - y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (45) - \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (45) = 0

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

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

= 0 - 2 x - 0

Simplify

= - 2 x

\frac{d}{d x} (sin (2 x - 2 π))

\int \frac{1}{x ^{2} + 2 x + 5} d x

\frac{\partial}{\partial x} (ln (x^{6} + 1) + y^{2})

\frac{d}{d x} (\frac{5}{12} (3 + 5) x^{3})

x \to - \infty lim (x^{0})

What is (\partial)/(\partial x)(45-x^2-y^2) ?
The answer to (\partial)/(\partial x)(45-x^2-y^2) is -2x