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Popular >

derivative of e^{2x}sin(2x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

derivative of ((sqrt(x))/(x+1))

\frac{d}{d x} (\frac{( x )}{x + 1})

derivative of (x^2+1e^{-x})

\frac{d}{d x} ((x^{2} + 1) e^{- x})

derivative of y=(7x-3)/(5x+4)+x^3 derivative of

y = \frac{7 x - 3}{5 x + 4} + x^{3}

integral of 8e^{2x}

\int 8 e^{2 x} d x

derivative of (x^2+5^3)

\frac{d}{d x} ((x^{2} + 5)^{3})

Frequently Asked Questions (FAQ)

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