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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{d}{d x} (\frac{8}{x - 5})

f (x) = - csc^{2} (x)

(x^{2} - y^{2}) d x + (2 x y) d y = 0

\int \frac{1}{- x ^{2} + 4 x - 3} d x

\int \frac{15}{4} x^{2} d x

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