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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x) = - 1

= 5 cos (y) e^{- x} (- 1)

Simplify

= - 5 e^{- x} cos (y)

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\int \frac{e ^{2 t}}{e ^{2 t} - 1} d t

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