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

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

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

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

- e^{- y} cos (π x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (- y) = - 1

= cos (π x) e^{- y} (- 1)

Simplify

= - e^{- y} cos (π x)

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