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Popular >

derivative of xe^xsin(2x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x} sin (2 x) + (e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x}) x

Simplify

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

Graph

Popular Examples

integral of (5x^4+3x^3-2)

\int (5 x^{4} + 3 x^{3} - 2) d x

integral of (sqrt(cos(θ))-2sin(θ))^2

\int (cos (θ) - 2 sin (θ))^{2} d θ

(x-y+2)dx-(x-y)dy=0

(x - y + 2) d x - (x - y) d y = 0

limit as x approaches 0 of (1+2x)^{5/x}

x \to 0 lim ((1 + 2 x)^{\frac{5}{x}})

tangent of 2x^3+2xy+2y^2=38,(-1,-4)tangent of

2 x^{3} + 2 x y + 2 y^{2} = 38, (- 1, - 4)

Frequently Asked Questions (FAQ)

What is the derivative of xe^xsin(2x) ?
The derivative of xe^xsin(2x) is e^xsin(2x)+x(e^xsin(2x)+2e^xcos(2x))
What is the first derivative of xe^xsin(2x) ?
The first derivative of xe^xsin(2x) is e^xsin(2x)+x(e^xsin(2x)+2e^xcos(2x))