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Popular >

derivative of x^2e^xcos(2x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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\int_{- 6}^{6} 58

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x \to 4 lim (\frac{∣ x ∣}{x})

Frequently Asked Questions (FAQ)

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