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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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