What is the derivative of e^xsin(5x) ?

The derivative of e^xsin(5x) is e^xsin(5x)+cos(5x)*5e^x

What is the first derivative of e^xsin(5x) ?

The first derivative of e^xsin(5x) is e^xsin(5x)+cos(5x)*5e^x

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\frac{d}{d x} (e^{x} sin (5 x))

e^{x} sin (5 x) + cos (5 x) \cdot 5 e^{x}

Solution steps

\frac{d}{d x} (e^{x} sin (5 x))

Apply the Product Rule:

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

f = e^{x}, g = sin (5 x)

= \frac{d}{d x} (e^{x}) sin (5 x) + \frac{d}{d x} (sin (5 x)) e^{x}

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= e^{x} sin (5 x) + cos (5 x) \cdot 5 e^{x}

What is the derivative of e^xsin(5x) ?
The derivative of e^xsin(5x) is e^xsin(5x)+cos(5x)*5e^x
What is the first derivative of e^xsin(5x) ?
The first derivative of e^xsin(5x) is e^xsin(5x)+cos(5x)*5e^x