What is the derivative of 60e^{-4.8x}sin(16x) ?

The derivative of 60e^{-4.8x}sin(16x) is 60(-4.8e^{-4.8x}sin(16x)+16e^{-4.8x}cos(16x))

What is the first derivative of 60e^{-4.8x}sin(16x) ?

The first derivative of 60e^{-4.8x}sin(16x) is 60(-4.8e^{-4.8x}sin(16x)+16e^{-4.8x}cos(16x))

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\frac{d}{d x} (60 e^{- 4.8 x} sin (16 x))

60 (- 4.8 e^{- 4.8 x} sin (16 x) + 16 e^{- 4.8 x} cos (16 x))

Solution steps

\frac{d}{d x} (60 e^{- 4.8 x} sin (16 x))

Take the constant out:

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

= 60 \frac{d}{d x} (e^{- 4.8 x} sin (16 x))

Apply the Product Rule:

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

f = e^{- 4.8 x}, g = sin (16 x)

= 60 (\frac{d}{d x} (e^{- 4.8 x}) sin (16 x) + \frac{d}{d x} (sin (16 x)) e^{- 4.8 x})

\frac{d}{d x} (e^{- 4.8 x}) = - 4.8 e^{- 4.8 x}

\frac{d}{d x} (sin (16 x)) = cos (16 x) \cdot 16

= 60 ((- 4.8 e^{- 4.8 x}) sin (16 x) + cos (16 x) \cdot 16 e^{- 4.8 x})

Simplify

= 60 (- 4.8 e^{- 4.8 x} sin (16 x) + 16 e^{- 4.8 x} cos (16 x))

x = y^{2}, x = 9

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What is the derivative of 60e^{-4.8x}sin(16x) ?
The derivative of 60e^{-4.8x}sin(16x) is 60(-4.8e^{-4.8x}sin(16x)+16e^{-4.8x}cos(16x))
What is the first derivative of 60e^{-4.8x}sin(16x) ?
The first derivative of 60e^{-4.8x}sin(16x) is 60(-4.8e^{-4.8x}sin(16x)+16e^{-4.8x}cos(16x))