What is (\partial)/(\partial x)(e^{-5x}cos(7pit)) ?

The answer to (\partial)/(\partial x)(e^{-5x}cos(7pit)) is -5e^{-5x}cos(7pit)

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(\partial)/(\partial x)(e^{-5x}cos(7pit))

\frac{\partial}{\partial x} (e^{- 5 x} cos (7 π t))

- 5 e^{- 5 x} cos (7 π t)

Solution steps

\frac{\partial}{\partial x} (e^{- 5 x} cos (7 π t))

Treat

t

as a constant

Take the constant out:

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

= cos (7 π t) \frac{\partial}{\partial x} (e^{- 5 x})

Apply the chain rule:

e^{- 5 x} \frac{\partial}{\partial x} (- 5 x)

= e^{- 5 x} \frac{\partial}{\partial x} (- 5 x)

\frac{\partial}{\partial x} (- 5 x) = - 5

= cos (7 π t) e^{- 5 x} (- 5)

Simplify

= - 5 e^{- 5 x} cos (7 π t)

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What is (\partial)/(\partial x)(e^{-5x}cos(7pit)) ?
The answer to (\partial)/(\partial x)(e^{-5x}cos(7pit)) is -5e^{-5x}cos(7pit)