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)

\frac{d}{d x} ((x - 1) (x^{2} - 8 x + 7))

y = 5 cos (2 x), y = 5 sin (4 x), x = 0, x = \frac{π}{4}

cos (\frac{t}{2})

\frac{22.96}{( s + 10.7 )}

x \to 2 lim (\frac{sin ( x )}{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)