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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int x^{2} (1 - x^{3})^{4} d x

\frac{s ^{2} - 2 s + 3}{( s - 2 ) ^{3}}

\int \frac{5 x + 3}{x ^{2} - 9} d x

\int x^{3} sin (6 x) d x

f (x) = x^{2} - \frac{1}{x}

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