What is the derivative of x^2e^{5x} ?

The derivative of x^2e^{5x} is 2xe^{5x}+e^{5x}*5x^2

What is the first derivative of x^2e^{5x} ?

The first derivative of x^2e^{5x} is 2xe^{5x}+e^{5x}*5x^2

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\frac{d}{d x} (x^{2} e^{5 x})

2 x e^{5 x} + e^{5 x} \cdot 5 x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{5 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{5 x}

= \frac{d}{d x} (x^{2}) e^{5 x} + \frac{d}{d x} (e^{5 x}) x^{2}

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

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

= 2 x e^{5 x} + e^{5 x} \cdot 5 x^{2}

7 + 4 x

\int_{0}^{4} - x^{2} d x

x \to 2 lim (4 - 2 x)

\frac{d y}{d x} - y = 3 e^{x} + 12 e^{4 x}

\int x^{2} \cdot 16 - x^{2} d x

What is the derivative of x^2e^{5x} ?
The derivative of x^2e^{5x} is 2xe^{5x}+e^{5x}*5x^2
What is the first derivative of x^2e^{5x} ?
The first derivative of x^2e^{5x} is 2xe^{5x}+e^{5x}*5x^2