What is (\partial)/(\partial x)(x+1/2 y) ?

The answer to (\partial)/(\partial x)(x+1/2 y) is 1

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(\partial)/(\partial x)(x+1/2 y)

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

1

Solution steps

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

Simplify

x + \frac{1}{2} y : x + \frac{y}{2}

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 1 + 0

Simplify

= 1

\frac{1}{1 - x}, 1.1

\frac{d y}{d x}, y = 1.1 x + 0.077 x^{2}

\frac{3}{( s + 2 ) \cdot ( 4 s ^{2} + 4 s + 5 )}

\frac{d}{d x} (x^{4} - 3 x^{3} + 2 x^{2})

x \to 4 lim (\frac{8 x - 4}{x + 6})

What is (\partial)/(\partial x)(x+1/2 y) ?
The answer to (\partial)/(\partial x)(x+1/2 y) is 1