What is the derivative of 3x^2e^x ?

The derivative of 3x^2e^x is 3(2xe^x+e^xx^2)

What is the first derivative of 3x^2e^x ?

The first derivative of 3x^2e^x is 3(2xe^x+e^xx^2)

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derivative of

3 x^{2} e^{x}

3 (2 x e^{x} + e^{x} x^{2})

Solution steps

\frac{d}{d x} (3 x^{2} e^{x})

Take the constant out:

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

= 3 \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}

= 3 (\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}

= 3 (2 x e^{x} + e^{x} x^{2})

\int 2 sin (x) + x d x

\frac{d}{d x} (5 x + \frac{3}{x})

x \to 0 lim (sin (x) ln (3 x))

(\frac{1}{4} x^{8} - 3 e^{x} + 100 ln (x))^{^{'}}

\frac{d}{d x} (0.0125 x^{2} - 1.15 x + 22.85)

What is the derivative of 3x^2e^x ?
The derivative of 3x^2e^x is 3(2xe^x+e^xx^2)
What is the first derivative of 3x^2e^x ?
The first derivative of 3x^2e^x is 3(2xe^x+e^xx^2)