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

The derivative of e^{-x}cos(x/2) is -e^{-x}cos(x/2)-1/2 e^{-x}sin(x/2)

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

The first derivative of e^{-x}cos(x/2) is -e^{-x}cos(x/2)-1/2 e^{-x}sin(x/2)

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

- e^{- x} cos (\frac{x}{2}) - \frac{1}{2} e^{- x} sin (\frac{x}{2})

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (cos (\frac{x}{2})) = - sin (\frac{x}{2}) \frac{1}{2}

= (- e^{- x}) cos (\frac{x}{2}) + (- sin (\frac{x}{2}) \frac{1}{2}) e^{- x}

Simplify

= - e^{- x} cos (\frac{x}{2}) - \frac{1}{2} e^{- x} sin (\frac{x}{2})

\frac{\partial}{\partial v} (3 u sin (v))

\frac{d y}{d x} + y^{3} x + 6 y = 0

x \to 0 lim (cos (2 x))

\int_{y}^{x} cos (t^{3}) d t

\frac{d}{d x} (4 - 2 sin (x))

What is the derivative of e^{-x}cos(x/2) ?
The derivative of e^{-x}cos(x/2) is -e^{-x}cos(x/2)-1/2 e^{-x}sin(x/2)
What is the first derivative of e^{-x}cos(x/2) ?
The first derivative of e^{-x}cos(x/2) is -e^{-x}cos(x/2)-1/2 e^{-x}sin(x/2)