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Popular >

derivative of x^3e^xcos(x)

Solution

derivative of

x^{3} e^{x} cos (x)

Solution

3 x^{2} e^{x} cos (x) + (e^{x} cos (x) - e^{x} sin (x)) x^{3}

Solution steps

\frac{d}{d x} (x^{3} e^{x} cos (x))

Apply the Product Rule:

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

f = x^{3}, g = e^{x} cos (x)

= \frac{d}{d x} (x^{3}) e^{x} cos (x) + \frac{d}{d x} (e^{x} cos (x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} e^{x} cos (x) + (e^{x} cos (x) - e^{x} sin (x)) x^{3}

Popular Examples

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Frequently Asked Questions (FAQ)

What is the derivative of x^3e^xcos(x) ?
The derivative of x^3e^xcos(x) is 3x^2e^xcos(x)+(e^xcos(x)-e^xsin(x))x^3
What is the first derivative of x^3e^xcos(x) ?
The first derivative of x^3e^xcos(x) is 3x^2e^xcos(x)+(e^xcos(x)-e^xsin(x))x^3