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

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

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

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

- e^{- x} cos (x) - e^{- x} sin (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x}, g = cos (x)

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

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

\frac{\partial}{\partial x} (cos (x)) = - sin (x)

= (- e^{- x}) cos (x) + (- sin (x)) e^{- x}

Simplify

= - e^{- x} cos (x) - e^{- x} sin (x)

9 y ln (x) - x y^{^{'}} = 0

36 y^{^{''}} + 84 y^{^{'}} + 49 y = 0

(x sin (3 x))^{^{'}}

\frac{d}{d x} (\frac{tan ( x )}{cos ( x ) - 4 x})

e^{8 x y}

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