What is the derivative of e^xsin(6x) ?

The derivative of e^xsin(6x) is e^xsin(6x)+cos(6x)*6e^x

What is the first derivative of e^xsin(6x) ?

The first derivative of e^xsin(6x) is e^xsin(6x)+cos(6x)*6e^x

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\frac{d}{d x} (e^{x} sin (6 x))

e^{x} sin (6 x) + cos (6 x) \cdot 6 e^{x}

Solution steps

\frac{d}{d x} (e^{x} sin (6 x))

Apply the Product Rule:

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

f = e^{x}, g = sin (6 x)

= \frac{d}{d x} (e^{x}) sin (6 x) + \frac{d}{d x} (sin (6 x)) e^{x}

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

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= e^{x} sin (6 x) + cos (6 x) \cdot 6 e^{x}

What is the derivative of e^xsin(6x) ?
The derivative of e^xsin(6x) is e^xsin(6x)+cos(6x)*6e^x
What is the first derivative of e^xsin(6x) ?
The first derivative of e^xsin(6x) is e^xsin(6x)+cos(6x)*6e^x