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

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

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

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

- e^{- y} cos (x)

Solution steps

\frac{\partial}{\partial y} (e^{- 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^{- 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 (x) e^{- y} (- 1)

Simplify

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

\frac{d}{d x} (ln (\frac{x ^{2}}{1 + x ^{2}}))

\frac{d}{d x} (2 x^{3} ln (3 x - 2))

\frac{d y}{d x}, 2 (x^{2} + y^{2}) 2 = 25 (x^{2} - y^{2})

\frac{\partial}{\partial y} (- 5 y^{6} sin (5 x))

\frac{d}{d x} (50 (80 - x)^{2})

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