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

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

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

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

- 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{1}{2} x))

Simplify

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

= \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})

x \to 0 lim (x^{8 s i n (x)})

(x 1 - x^{2})^{^{'}}

\int \frac{sec ^{2} ( y )}{tan ( y )} d y

\frac{d}{d x} (sin^{2} (tan (4 x)))

\int tan (θ) sec (θ) d θ

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