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Popular >

derivative of xe^xsin(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

derivative of (3x+4^4)

\frac{d}{d x} ((3 x + 4)^{4})

derivative of 3cosh(3x-sinh(3x))

\frac{d}{d x} (3 cosh (3 x) - sinh (3 x))

limit as x approaches infinity of e^{4x}

x \to \infty lim (e^{4 x})

(\partial)/(\partial x)(5y^3e^{x-2}-2xy)

\frac{\partial}{\partial x} (5 y^{3} e^{x - 2} - 2 x y)

integral of (xe^{-x^2}+(e^x)/(e^x+3))

\int (x e^{- x^{2}} + \frac{e ^{x}}{e ^{x} + 3}) d x

Frequently Asked Questions (FAQ)

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