What is the derivative of e^{-4x}sin(3x) ?

The derivative of e^{-4x}sin(3x) is -4e^{-4x}sin(3x)+3e^{-4x}cos(3x)

What is the first derivative of e^{-4x}sin(3x) ?

The first derivative of e^{-4x}sin(3x) is -4e^{-4x}sin(3x)+3e^{-4x}cos(3x)

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\frac{d}{d x} (e^{- 4 x} sin (3 x))

- 4 e^{- 4 x} sin (3 x) + 3 e^{- 4 x} cos (3 x)

Solution steps

\frac{d}{d x} (e^{- 4 x} sin (3 x))

Apply the Product Rule:

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

f = e^{- 4 x}, g = sin (3 x)

= \frac{d}{d x} (e^{- 4 x}) sin (3 x) + \frac{d}{d x} (sin (3 x)) e^{- 4 x}

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

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

= (- 4 e^{- 4 x}) sin (3 x) + cos (3 x) \cdot 3 e^{- 4 x}

Simplify

= - 4 e^{- 4 x} sin (3 x) + 3 e^{- 4 x} cos (3 x)

\frac{d y}{d x} = \frac{1 - x y ^{2}}{2 x ^{2} y}

\frac{\partial}{\partial x} (z (2 x y))

y^{^{'}} + y - 2 = 0

x \to 2 lim (2 x^{2} - 7 x + 4)

\int tan^{3} (θ) d θ

What is the derivative of e^{-4x}sin(3x) ?
The derivative of e^{-4x}sin(3x) is -4e^{-4x}sin(3x)+3e^{-4x}cos(3x)
What is the first derivative of e^{-4x}sin(3x) ?
The first derivative of e^{-4x}sin(3x) is -4e^{-4x}sin(3x)+3e^{-4x}cos(3x)