What is the derivative of e^xsin(9x) ?

The derivative of e^xsin(9x) is e^xsin(9x)+cos(9x)*9e^x

What is the first derivative of e^xsin(9x) ?

The first derivative of e^xsin(9x) is e^xsin(9x)+cos(9x)*9e^x

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\frac{d}{d x} (e^{x} sin (9 x))

e^{x} sin (9 x) + cos (9 x) \cdot 9 e^{x}

Solution steps

\frac{d}{d x} (e^{x} sin (9 x))

Apply the Product Rule:

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

f = e^{x}, g = sin (9 x)

= \frac{d}{d x} (e^{x}) sin (9 x) + \frac{d}{d x} (sin (9 x)) e^{x}

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

\frac{d}{d x} (sin (9 x)) = cos (9 x) \cdot 9

= e^{x} sin (9 x) + cos (9 x) \cdot 9 e^{x}

What is the derivative of e^xsin(9x) ?
The derivative of e^xsin(9x) is e^xsin(9x)+cos(9x)*9e^x
What is the first derivative of e^xsin(9x) ?
The first derivative of e^xsin(9x) is e^xsin(9x)+cos(9x)*9e^x