What is the derivative of y=e^{-x}cos(2x) ?

The derivative of y=e^{-x}cos(2x) is -e^{-x}cos(2x)-2e^{-x}sin(2x)

What is the first derivative of y=e^{-x}cos(2x) ?

The first derivative of y=e^{-x}cos(2x) is -e^{-x}cos(2x)-2e^{-x}sin(2x)

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derivative of

y = e^{- x} cos (2 x)

- e^{- x} cos (2 x) - 2 e^{- x} sin (2 x)

Solution steps

\frac{d}{d x} (e^{- x} cos (2 x))

Apply the Product Rule:

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

f = e^{- x}, g = cos (2 x)

= \frac{d}{d x} (e^{- x}) cos (2 x) + \frac{d}{d x} (cos (2 x)) e^{- x}

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= (- e^{- x}) cos (2 x) + (- sin (2 x) \cdot 2) e^{- x}

Simplify

= - e^{- x} cos (2 x) - 2 e^{- x} sin (2 x)

\frac{1}{s ^{4} + s ^{2}}

\int (x^{2} + 2 x) d x

\frac{d}{d t} (t e^{4 t})

\int - 3 tan (3 y) d y

\frac{d}{d x} (\frac{x - y}{sin ( x ) - sin ( y )})

What is the derivative of y=e^{-x}cos(2x) ?
The derivative of y=e^{-x}cos(2x) is -e^{-x}cos(2x)-2e^{-x}sin(2x)
What is the first derivative of y=e^{-x}cos(2x) ?
The first derivative of y=e^{-x}cos(2x) is -e^{-x}cos(2x)-2e^{-x}sin(2x)