What is the derivative of e^{-3x}y ?

The derivative of e^{-3x}y is -3e^{-3x}y+e^{-3x}(dy)/(dx)

What is the first derivative of e^{-3x}y ?

The first derivative of e^{-3x}y is -3e^{-3x}y+e^{-3x}(dy)/(dx)

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

- 3 e^{- 3 x} y + e^{- 3 x} \frac{d y}{d x}

Solution steps

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

Apply the Product Rule:

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

f = e^{- 3 x}, g = y

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

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

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

Simplify

= - 3 e^{- 3 x} y + e^{- 3 x} \frac{d y}{d x}

What is the derivative of e^{-3x}y ?
The derivative of e^{-3x}y is -3e^{-3x}y+e^{-3x}(dy)/(dx)
What is the first derivative of e^{-3x}y ?
The first derivative of e^{-3x}y is -3e^{-3x}y+e^{-3x}(dy)/(dx)