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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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