What is the derivative of f(x)=x^2e^x ?

The derivative of f(x)=x^2e^x is 2xe^x+e^xx^2

What is the first derivative of f(x)=x^2e^x ?

The first derivative of f(x)=x^2e^x is 2xe^x+e^xx^2

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derivative of

f (x) = x^{2} e^{x}

2 x e^{x} + e^{x} x^{2}

Solution steps

\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}

= \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}

= 2 x e^{x} + e^{x} x^{2}

\int \frac{10}{x ^{2} + 8 x + 15} d x

\frac{\partial}{\partial x} (y e^{y} - x e^{x})

x \to 3 lim (x^{2} - 5 x + 6)

(y^{3} - 2 x^{2} y) d x + (2 x^{3}) d y = 0

\frac{6 s + 3}{s ^{4} + 5 s ^{2} + 4}

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