What is (\partial)/(\partial x)(xy-x-3y) ?

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

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(\partial)/(\partial x)(xy-x-3y)

\frac{\partial}{\partial x} (x y - x - 3 y)

y - 1

Solution steps

\frac{\partial}{\partial x} (x y - x - 3 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= y - 1 - 0

Simplify

= y - 1

\int \frac{1 + sin ( x )}{1 + sin ( x ) - cos ( x )} d x

\int \frac{7}{x ^{3}} d x

y = x^{10} e^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y = t^{2}

2 x y d x - (1 + y) d y = 0

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