What is (\partial)/(\partial y)(e^{-1x}cos(6y)) ?

The answer to (\partial)/(\partial y)(e^{-1x}cos(6y)) is -6e^{-x}sin(6y)

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(\partial)/(\partial y)(e^{-1x}cos(6y))

\frac{\partial}{\partial y} (e^{- 1 x} cos (6 y))

- 6 e^{- x} sin (6 y)

Solution steps

\frac{\partial}{\partial y} (e^{- 1 \cdot x} cos (6 y))

Simplify

e^{- 1 \cdot x} cos (6 y) : e^{- x} cos (6 y)

= \frac{\partial}{\partial y} (e^{- x} cos (6 y))

Treat

x

as a constant

Take the constant out:

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

= e^{- x} \frac{\partial}{\partial y} (cos (6 y))

Apply the chain rule:

- sin (6 y) \frac{\partial}{\partial y} (6 y)

= - sin (6 y) \frac{\partial}{\partial y} (6 y)

\frac{\partial}{\partial y} (6 y) = 6

= e^{- x} (- sin (6 y) \cdot 6)

Simplify

= - 6 e^{- x} sin (6 y)

What is (\partial)/(\partial y)(e^{-1x}cos(6y)) ?
The answer to (\partial)/(\partial y)(e^{-1x}cos(6y)) is -6e^{-x}sin(6y)