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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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\int \frac{tan ^{2} ( θ )}{sec ( θ )} d θ

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\int \frac{5}{x ( 7 + 5 x ) ^{6}} d x

Frequently Asked Questions (FAQ)

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