What is the derivative of e^x*sin(2x) ?

The derivative of e^x*sin(2x) is e^xsin(2x)+cos(2x)*2e^x

What is the first derivative of e^x*sin(2x) ?

The first derivative of e^x*sin(2x) is e^xsin(2x)+cos(2x)*2e^x

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\frac{d}{d x} (e^{x} \cdot sin (2 x))

e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x}

Solution steps

\frac{d}{d x} (e^{x} sin (2 x))

Apply the Product Rule:

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

f = e^{x}, g = sin (2 x)

= \frac{d}{d x} (e^{x}) sin (2 x) + \frac{d}{d x} (sin (2 x)) e^{x}

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

= e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x}

\frac{d}{d x} (8 x - x^{2})

\int 6 cos (6 x) - 5 d x

\frac{\partial}{\partial x} (x - 1)

\frac{7}{1 + x}

\frac{\partial}{\partial x} (3 x^{2} y - 1)

What is the derivative of e^x*sin(2x) ?
The derivative of e^x*sin(2x) is e^xsin(2x)+cos(2x)*2e^x
What is the first derivative of e^x*sin(2x) ?
The first derivative of e^x*sin(2x) is e^xsin(2x)+cos(2x)*2e^x