What is the derivative of Ax^2e^x ?

The derivative of Ax^2e^x is A(2xe^x+e^xx^2)

What is the first derivative of Ax^2e^x ?

The first derivative of Ax^2e^x is A(2xe^x+e^xx^2)

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

A (2 x e^{x} + e^{x} x^{2})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

= A (2 x e^{x} + e^{x} x^{2})

\int_{0}^{3} 450.268 e^{1.12567 t} d t

x \to \infty lim (e^{x} - x)

\int \frac{x ^{2} + 1}{x ^{4} + 1} d x

2 e^{x} cos (x)

\frac{\partial}{\partial x} (ln (x^{3}))

What is the derivative of Ax^2e^x ?
The derivative of Ax^2e^x is A(2xe^x+e^xx^2)
What is the first derivative of Ax^2e^x ?
The first derivative of Ax^2e^x is A(2xe^x+e^xx^2)