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

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

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

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

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

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

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

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