What is the derivative of e^{4x}sin(x) ?

The derivative of e^{4x}sin(x) is e^{4x}*4sin(x)+cos(x)e^{4x}

What is the first derivative of e^{4x}sin(x) ?

The first derivative of e^{4x}sin(x) is e^{4x}*4sin(x)+cos(x)e^{4x}

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\frac{d}{d x} (e^{4 x} sin (x))

e^{4 x} \cdot 4 sin (x) + cos (x) e^{4 x}

Solution steps

\frac{d}{d x} (e^{4 x} sin (x))

Apply the Product Rule:

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

f = e^{4 x}, g = sin (x)

= \frac{d}{d x} (e^{4 x}) sin (x) + \frac{d}{d x} (sin (x)) e^{4 x}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

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

= e^{4 x} \cdot 4 sin (x) + cos (x) e^{4 x}

What is the derivative of e^{4x}sin(x) ?
The derivative of e^{4x}sin(x) is e^{4x}*4sin(x)+cos(x)e^{4x}
What is the first derivative of e^{4x}sin(x) ?
The first derivative of e^{4x}sin(x) is e^{4x}*4sin(x)+cos(x)e^{4x}