What is the derivative of e^{-4x}cos(4x) ?

The derivative of e^{-4x}cos(4x) is -4e^{-4x}cos(4x)-4e^{-4x}sin(4x)

What is the first derivative of e^{-4x}cos(4x) ?

The first derivative of e^{-4x}cos(4x) is -4e^{-4x}cos(4x)-4e^{-4x}sin(4x)

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\frac{d}{d x} (e^{- 4 x} cos (4 x))

- 4 e^{- 4 x} cos (4 x) - 4 e^{- 4 x} sin (4 x)

Solution steps

\frac{d}{d x} (e^{- 4 x} cos (4 x))

Apply the Product Rule:

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

f = e^{- 4 x}, g = cos (4 x)

= \frac{d}{d x} (e^{- 4 x}) cos (4 x) + \frac{d}{d x} (cos (4 x)) e^{- 4 x}

\frac{d}{d x} (e^{- 4 x}) = - 4 e^{- 4 x}

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= (- 4 e^{- 4 x}) cos (4 x) + (- sin (4 x) \cdot 4) e^{- 4 x}

Simplify

= - 4 e^{- 4 x} cos (4 x) - 4 e^{- 4 x} sin (4 x)

\frac{\partial}{\partial x} (3 x^{4})

y = 6 x^{2} - x^{3}

\frac{d y}{d x} = x + y - 1

\int (7 cos (x)) d x

x \to 0 lim (\frac{( x + 2 ) ^{3} - 8}{x})

What is the derivative of e^{-4x}cos(4x) ?
The derivative of e^{-4x}cos(4x) is -4e^{-4x}cos(4x)-4e^{-4x}sin(4x)
What is the first derivative of e^{-4x}cos(4x) ?
The first derivative of e^{-4x}cos(4x) is -4e^{-4x}cos(4x)-4e^{-4x}sin(4x)