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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (2 y) \frac{\partial}{\partial y} (2 y)

= - sin (2 y) \frac{\partial}{\partial y} (2 y)

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

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

Simplify

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

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