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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- 6 x) = - 6

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

Simplify

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

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