What is the derivative of 2xe^xcos(x) ?

The derivative of 2xe^xcos(x) is 2(e^xcos(x)+x(e^xcos(x)-e^xsin(x)))

What is the first derivative of 2xe^xcos(x) ?

The first derivative of 2xe^xcos(x) is 2(e^xcos(x)+x(e^xcos(x)-e^xsin(x)))

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derivative of

2 x e^{x} cos (x)

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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)

= 2 (\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)

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

Simplify

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

\frac{d}{d x} (ln (\frac{x ^{\frac{1}{2}}}{3}))

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

f (x) = ln (x^{3})

3 e^{3 t}

\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

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