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

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

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

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

- e^{- x} sin (y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

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

Simplify

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

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