What is (\partial)/(\partial x)(5-x^2+xy-2^2) ?

The answer to (\partial)/(\partial x)(5-x^2+xy-2^2) is y-2x

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(\partial)/(\partial x)(5-x^2+xy-2^2)

\frac{\partial}{\partial x} (5 - x^{2} + x y - 2^{2})

y - 2 x

Solution steps

\frac{\partial}{\partial x} (5 - x^{2} + x y - 2^{2})

Simplify

5 - x^{2} + x y - 2^{2} : - x^{2} + x y + 1

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

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

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

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

= - 2 x + y + 0

Simplify

= y - 2 x

\frac{d}{d x} ((x^{3} + 4)^{- 3})

x \to 0 + lim (6 - \frac{1}{x ^{2}})

y = 4 x^{\frac{2}{3}} + 6 x^{\frac{1}{2}} - 8

\int 8 x + 3 d x

\frac{d r}{d θ} + r tan (θ) = sec (θ)

What is (\partial)/(\partial x)(5-x^2+xy-2^2) ?
The answer to (\partial)/(\partial x)(5-x^2+xy-2^2) is y-2x