What is the derivative of e^{-2x}*cos(3x) ?

The derivative of e^{-2x}*cos(3x) is -2e^{-2x}cos(3x)-3e^{-2x}sin(3x)

What is the first derivative of e^{-2x}*cos(3x) ?

The first derivative of e^{-2x}*cos(3x) is -2e^{-2x}cos(3x)-3e^{-2x}sin(3x)

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\frac{d}{d x} (e^{- 2 x} \cdot cos (3 x))

- 2 e^{- 2 x} cos (3 x) - 3 e^{- 2 x} sin (3 x)

Solution steps

\frac{d}{d x} (e^{- 2 x} cos (3 x))

Apply the Product Rule:

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

f = e^{- 2 x}, g = cos (3 x)

= \frac{d}{d x} (e^{- 2 x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{- 2 x}

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= (- 2 e^{- 2 x}) cos (3 x) + (- sin (3 x) \cdot 3) e^{- 2 x}

Simplify

= - 2 e^{- 2 x} cos (3 x) - 3 e^{- 2 x} sin (3 x)

x \to 0 + lim (3 + x^{5} ln (x))

\frac{\partial}{\partial y} (x^{3} + y z^{2})

\int \frac{1}{x - 2} d x

\frac{d}{d x} (csc (cot (x)))

x \to 1 + lim (\frac{x + 2}{x - 1})

What is the derivative of e^{-2x}*cos(3x) ?
The derivative of e^{-2x}*cos(3x) is -2e^{-2x}cos(3x)-3e^{-2x}sin(3x)
What is the first derivative of e^{-2x}*cos(3x) ?
The first derivative of e^{-2x}*cos(3x) is -2e^{-2x}cos(3x)-3e^{-2x}sin(3x)