What is (\partial)/(\partial x)(ze^{x+y}-xy) ?

The answer to (\partial)/(\partial x)(ze^{x+y}-xy) is ze^{x+y}-y

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(\partial)/(\partial x)(ze^{x+y}-xy)

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

z e^{x + y} - y

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (z e^{x + y}) - \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (z e^{x + y}) = z e^{x + y}

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

= z e^{x + y} - y

\frac{d}{d x} ((x + 1) (x + 1 - \frac{1}{x + 2}))

\int_{0}^{π} 3 sin^{4} (3 t) d t

\frac{15}{( s + 10 ) ( s + 11 )}

\int_{0}^{2.8} 0.2 x d x

\frac{4 π r ^{3}}{3}

What is (\partial)/(\partial x)(ze^{x+y}-xy) ?
The answer to (\partial)/(\partial x)(ze^{x+y}-xy) is ze^{x+y}-y