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

The derivative of f(x)=x^5e^x is 5x^4e^x+e^xx^5

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

The first derivative of f(x)=x^5e^x is 5x^4e^x+e^xx^5

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derivative of

f (x) = 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}

\frac{\partial}{\partial x} (21 x^{3} cos (7 x^{2} y))

\int \frac{1}{x ^{2} - 16} d x

x \to + 2 - lim (6 - 3 x - 3)

\frac{d}{d x} (x^{1 - x})

11 x

What is the derivative of f(x)=x^5e^x ?
The derivative of f(x)=x^5e^x is 5x^4e^x+e^xx^5
What is the first derivative of f(x)=x^5e^x ?
The first derivative of f(x)=x^5e^x is 5x^4e^x+e^xx^5