What is (\partial)/(\partial x)(-1/2 x-3y+1) ?

The answer to (\partial)/(\partial x)(-1/2 x-3y+1) is -1/2

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(\partial)/(\partial x)(-1/2 x-3y+1)

\frac{\partial}{\partial x} (- \frac{1}{2} x - 3 y + 1)

- \frac{1}{2}

Solution steps

\frac{\partial}{\partial x} (- \frac{1}{2} x - 3 y + 1)

Simplify

- \frac{1}{2} x - 3 y + 1 : - \frac{x}{2} - 3 y + 1

= \frac{\partial}{\partial x} (- \frac{x}{2} - 3 y + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial x} (\frac{x}{2}) - \frac{\partial}{\partial x} (3 y) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (\frac{x}{2}) = \frac{1}{2}

\frac{\partial}{\partial x} (3 y) = 0

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

= - \frac{1}{2} - 0 + 0

Simplify

= - \frac{1}{2}

x \to 1 lim (3 + x^{2})

f (x) = \frac{1}{x ^{4}}

y d x = x d y

\int \frac{sin ( θ ) cos ( θ )}{1 + sin ^{2} ( θ )} d θ

\frac{\partial}{\partial x} (x^{3} + y^{3})

What is (\partial)/(\partial x)(-1/2 x-3y+1) ?
The answer to (\partial)/(\partial x)(-1/2 x-3y+1) is -1/2