What is (\partial)/(\partial x)(e^{xy}cos(2x)-3y) ?

The answer to (\partial)/(\partial x)(e^{xy}cos(2x)-3y) is e^{xy}ycos(2x)-2e^{xy}sin(2x)

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(\partial)/(\partial x)(e^{xy}cos(2x)-3y)

\frac{\partial}{\partial x} (e^{x y} cos (2 x) - 3 y)

e^{x y} y cos (2 x) - 2 e^{x y} sin (2 x)

Solution steps

\frac{\partial}{\partial x} (e^{x y} cos (2 x) - 3 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e^{x y} cos (2 x)) - \frac{\partial}{\partial x} (3 y)

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

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

= y e^{y x} cos (2 x) - 2 e^{y x} sin (2 x) - 0

Simplify

= e^{x y} y cos (2 x) - 2 e^{x y} sin (2 x)

1^{^{'}}

x \to 2 + lim (\frac{3 x}{x - 2})

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

\frac{1}{5 x ^{2} + 3 x}

10 y^{^{''}} + 1000 y = 130 cos (8 t)

What is (\partial)/(\partial x)(e^{xy}cos(2x)-3y) ?
The answer to (\partial)/(\partial x)(e^{xy}cos(2x)-3y) is e^{xy}ycos(2x)-2e^{xy}sin(2x)