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

The derivative of e^{-2x}(sin(3x+cos(3x))) is -5e^{-2x}sin(3x)+e^{-2x}cos(3x)

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

The first derivative of e^{-2x}(sin(3x+cos(3x))) is -5e^{-2x}sin(3x)+e^{-2x}cos(3x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- 2 e^{- 2 x}) (sin (3 x) + cos (3 x)) + (cos (3 x) \cdot 3 - sin (3 x) \cdot 3) e^{- 2 x} : - 5 e^{- 2 x} sin (3 x) + e^{- 2 x} cos (3 x)

= - 5 e^{- 2 x} sin (3 x) + e^{- 2 x} cos (3 x)

\frac{d}{d x} (- 8 sin (4 x))

x \to 3 + lim (x)

\int_{0}^{2} x^{2} e^{x^{3}} d x

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

\int \frac{y}{3} d y

What is the derivative of e^{-2x}(sin(3x+cos(3x))) ?
The derivative of e^{-2x}(sin(3x+cos(3x))) is -5e^{-2x}sin(3x)+e^{-2x}cos(3x)
What is the first derivative of e^{-2x}(sin(3x+cos(3x))) ?
The first derivative of e^{-2x}(sin(3x+cos(3x))) is -5e^{-2x}sin(3x)+e^{-2x}cos(3x)