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

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

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

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

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\frac{d}{d x} (5 e^{- 2 x} sin (3 x))

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

Solution steps

\frac{d}{d x} (5 e^{- 2 x} sin (3 x))

Take the constant out:

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

= 5 \frac{d}{d x} (e^{- 2 x} sin (3 x))

Apply the Product Rule:

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

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

= 5 (\frac{d}{d x} (e^{- 2 x}) sin (3 x) + \frac{d}{d x} (sin (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) \cdot 3

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

Simplify

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

(1 + x)^{- \frac{5}{3}}

\frac{\partial}{\partial x} (ln (x y))

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

x \to 9 lim (x + 7)

\frac{d}{d t} (1 0^{2 t})

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