What is the derivative of 2e^{-1.5x}cos(3x) ?

The derivative of 2e^{-1.5x}cos(3x) is 2(-1.5e^{-1.5x}cos(3x)-3e^{-1.5x}sin(3x))

What is the first derivative of 2e^{-1.5x}cos(3x) ?

The first derivative of 2e^{-1.5x}cos(3x) is 2(-1.5e^{-1.5x}cos(3x)-3e^{-1.5x}sin(3x))

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\frac{d}{d x} (2 e^{- 1.5 x} cos (3 x))

2 (- 1.5 e^{- 1.5 x} cos (3 x) - 3 e^{- 1.5 x} sin (3 x))

Solution steps

\frac{d}{d x} (2 e^{- 1.5 x} cos (3 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (e^{- 1.5 x} cos (3 x))

Apply the Product Rule:

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

f = e^{- 1.5 x}, g = cos (3 x)

= 2 (\frac{d}{d x} (e^{- 1.5 x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{- 1.5 x})

\frac{d}{d x} (e^{- 1.5 x}) = - 1.5 e^{- 1.5 x}

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

= 2 ((- 1.5 e^{- 1.5 x}) cos (3 x) + (- sin (3 x) \cdot 3) e^{- 1.5 x})

Simplify

= 2 (- 1.5 e^{- 1.5 x} cos (3 x) - 3 e^{- 1.5 x} sin (3 x))

What is the derivative of 2e^{-1.5x}cos(3x) ?
The derivative of 2e^{-1.5x}cos(3x) is 2(-1.5e^{-1.5x}cos(3x)-3e^{-1.5x}sin(3x))
What is the first derivative of 2e^{-1.5x}cos(3x) ?
The first derivative of 2e^{-1.5x}cos(3x) is 2(-1.5e^{-1.5x}cos(3x)-3e^{-1.5x}sin(3x))