What is the derivative of xe^xcos(x) ?

The derivative of xe^xcos(x) is e^xcos(x)+x(e^xcos(x)-e^xsin(x))

What is the first derivative of xe^xcos(x) ?

The first derivative of xe^xcos(x) is e^xcos(x)+x(e^xcos(x)-e^xsin(x))

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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