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

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

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

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

2 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y - 0

Simplify

= 2 y

y^{^{'}} = \frac{e ^{x + y}}{1 + e ^{x}}, y (1) = 0

\int 2^{2 - 2 x} d x

\int_{0}^{1} (e^{x} - x) d x

\frac{1}{x - 1}, 24

x = y (2 - y), x = - y

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