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Popular Calculus >

derivative of e^{3x}sin(2x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

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

Graph

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Frequently Asked Questions (FAQ)

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