What is the derivative of e^x(6x^2-12x+12) ?

The derivative of e^x(6x^2-12x+12) is 6e^xx^2

What is the first derivative of e^x(6x^2-12x+12) ?

The first derivative of e^x(6x^2-12x+12) is 6e^xx^2

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\frac{d}{d x} (e^{x} (6 x^{2} - 12 x + 12))

6 e^{x} x^{2}

Solution steps

\frac{d}{d x} (e^{x} (6 x^{2} - 12 x + 12))

Apply the Product Rule:

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

f = e^{x}, g = 6 x^{2} - 12 x + 12

= \frac{d}{d x} (e^{x}) (6 x^{2} - 12 x + 12) + \frac{d}{d x} (6 x^{2} - 12 x + 12) e^{x}

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

\frac{d}{d x} (6 x^{2} - 12 x + 12) = 12 x - 12

= e^{x} (6 x^{2} - 12 x + 12) + (12 x - 12) e^{x}

Simplify

e^{x} (6 x^{2} - 12 x + 12) + (12 x - 12) e^{x} : 6 e^{x} x^{2}

= 6 e^{x} x^{2}

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What is the derivative of e^x(6x^2-12x+12) ?
The derivative of e^x(6x^2-12x+12) is 6e^xx^2
What is the first derivative of e^x(6x^2-12x+12) ?
The first derivative of e^x(6x^2-12x+12) is 6e^xx^2