What is the derivative of e^{-6x}sin(6x) ?

The derivative of e^{-6x}sin(6x) is -6e^{-6x}sin(6x)+6e^{-6x}cos(6x)

What is the first derivative of e^{-6x}sin(6x) ?

The first derivative of e^{-6x}sin(6x) is -6e^{-6x}sin(6x)+6e^{-6x}cos(6x)

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Popular >

\frac{d}{d x} (e^{- 6 x} sin (6 x))

- 6 e^{- 6 x} sin (6 x) + 6 e^{- 6 x} cos (6 x)

Solution steps

\frac{d}{d x} (e^{- 6 x} sin (6 x))

Apply the Product Rule:

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

f = e^{- 6 x}, g = sin (6 x)

= \frac{d}{d x} (e^{- 6 x}) sin (6 x) + \frac{d}{d x} (sin (6 x)) e^{- 6 x}

\frac{d}{d x} (e^{- 6 x}) = - 6 e^{- 6 x}

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= (- 6 e^{- 6 x}) sin (6 x) + cos (6 x) \cdot 6 e^{- 6 x}

Simplify

= - 6 e^{- 6 x} sin (6 x) + 6 e^{- 6 x} cos (6 x)

\int \frac{y}{1 - 4 y ^{4}} d y

\frac{d}{d x} (4 x^{- 2 x})

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

\int \frac{1}{x ( 100 - x )} d x

\frac{d}{d x} (1 + x + x^{2})

What is the derivative of e^{-6x}sin(6x) ?
The derivative of e^{-6x}sin(6x) is -6e^{-6x}sin(6x)+6e^{-6x}cos(6x)
What is the first derivative of e^{-6x}sin(6x) ?
The first derivative of e^{-6x}sin(6x) is -6e^{-6x}sin(6x)+6e^{-6x}cos(6x)