What is (\partial)/(\partial x)(xe^{xy}-2y) ?

The answer to (\partial)/(\partial x)(xe^{xy}-2y) is e^{xy}+e^{xy}xy

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(\partial)/(\partial x)(xe^{xy}-2y)

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

e^{x y} + e^{x y} x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y x} + y e^{y x} x - 0

Simplify

= e^{x y} + e^{x y} x y

7 x e^{x} csc (x)

\int 2 x ln (x) d x

\int \frac{8 x - 3}{x ^{2} + x + 1} d x

x \to 0 + lim (\frac{∣ x ∣}{x})

f (x) = 7 + 4 x^{2} - 2 x^{3}, (2, 7)

What is (\partial)/(\partial x)(xe^{xy}-2y) ?
The answer to (\partial)/(\partial x)(xe^{xy}-2y) is e^{xy}+e^{xy}xy