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

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

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

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

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

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

Solution steps

\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)

= \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}) = e^{2 x} \cdot 2

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

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

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