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Popular >

derivative of e^{2x}sin(7x)

Solution

\frac{d}{d x} (e^{2 x} sin (7 x))

Solution

e^{2 x} \cdot 2 sin (7 x) + cos (7 x) \cdot 7 e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} sin (7 x))

Apply the Product Rule:

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

f = e^{2 x}, g = sin (7 x)

= \frac{d}{d x} (e^{2 x}) sin (7 x) + \frac{d}{d x} (sin (7 x)) e^{2 x}

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

\frac{d}{d x} (sin (7 x)) = cos (7 x) \cdot 7

= e^{2 x} \cdot 2 sin (7 x) + cos (7 x) \cdot 7 e^{2 x}

Graph

Popular Examples

(dy)/(dt)+e^ty=-7e^t

\frac{d y}{d t} + e^{t} y = - 7 e^{t}

integral of sin^2(1/2 pix)

\int sin^{2} (\frac{1}{2} π x) d x

taylor 5ln(x^2),x=1 taylor

5 ln (x^{2}), x = 1

integral of (9/x)

\int (\frac{9}{x}) d x

derivative of 2-7x

\frac{d}{d x} (2 - 7 x)

Frequently Asked Questions (FAQ)

What is the derivative of e^{2x}sin(7x) ?
The derivative of e^{2x}sin(7x) is e^{2x}*2sin(7x)+cos(7x)*7e^{2x}
What is the first derivative of e^{2x}sin(7x) ?
The first derivative of e^{2x}sin(7x) is e^{2x}*2sin(7x)+cos(7x)*7e^{2x}