What is the derivative of x^5e^xcos(x) ?

The derivative of x^5e^xcos(x) is 5x^4e^xcos(x)+(e^xcos(x)-e^xsin(x))x^5

What is the first derivative of x^5e^xcos(x) ?

The first derivative of x^5e^xcos(x) is 5x^4e^xcos(x)+(e^xcos(x)-e^xsin(x))x^5

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\frac{d}{d x} (x^{5} e^{x} cos (x))

5 x^{4} e^{x} cos (x) + (e^{x} cos (x) - e^{x} sin (x)) x^{5}

Solution steps

\frac{d}{d x} (x^{5} e^{x} cos (x))

Apply the Product Rule:

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

f = x^{5}, g = e^{x} cos (x)

= \frac{d}{d x} (x^{5}) e^{x} cos (x) + \frac{d}{d x} (e^{x} cos (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} e^{x} cos (x) + (e^{x} cos (x) - e^{x} sin (x)) x^{5}

What is the derivative of x^5e^xcos(x) ?
The derivative of x^5e^xcos(x) is 5x^4e^xcos(x)+(e^xcos(x)-e^xsin(x))x^5
What is the first derivative of x^5e^xcos(x) ?
The first derivative of x^5e^xcos(x) is 5x^4e^xcos(x)+(e^xcos(x)-e^xsin(x))x^5