What is the derivative of x^5e^x ?

The derivative of x^5e^x is 5x^4e^x+e^xx^5

What is the first derivative of x^5e^x ?

The first derivative of x^5e^x is 5x^4e^x+e^xx^5

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derivative of

x^{5} e^{x}

5 x^{4} e^{x} + e^{x} x^{5}

Solution steps

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

Apply the Product Rule:

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

f = x^{5}, g = e^{x}

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

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

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

= 5 x^{4} e^{x} + e^{x} x^{5}

\int 2 \cdot (x - 6)^{3} d x

\frac{d y}{d x} = 7 x^{6} e^{- y}

f (x) = 7 + 4 x^{2} - 2 x^{3}, at x = a

4 e^{x^{- 3}}

x \to 0 lim (9 x^{2} - 4 x + 8)

What is the derivative of x^5e^x ?
The derivative of x^5e^x is 5x^4e^x+e^xx^5
What is the first derivative of x^5e^x ?
The first derivative of x^5e^x is 5x^4e^x+e^xx^5