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

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

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

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

2 x

Solution steps

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

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

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

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

\frac{\partial}{\partial x} (5) = 0

= 2 x + 0 - 0

Simplify

= 2 x

\frac{d y}{d x} = 5 y e^{x + 2}

f (x) = 2 x^{2} - 7

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

x = \frac{1}{2} y^{2}, y = 1, y = - \frac{1}{2} x + 3

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

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