What is the derivative of (3x^2-6x+6e^x) ?

The derivative of (3x^2-6x+6e^x) is 3e^xx^2

What is the first derivative of (3x^2-6x+6e^x) ?

The first derivative of (3x^2-6x+6e^x) is 3e^xx^2

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\frac{d}{d x} ((3 x^{2} - 6 x + 6) e^{x})

3 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((3 x^{2} - 6 x + 6) e^{x})

Apply the Product Rule:

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

f = 3 x^{2} - 6 x + 6, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 6 x + 6) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 6 x + 6)

\frac{d}{d x} (3 x^{2} - 6 x + 6) = 6 x - 6

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

= (6 x - 6) e^{x} + e^{x} (3 x^{2} - 6 x + 6)

Simplify

(6 x - 6) e^{x} + e^{x} (3 x^{2} - 6 x + 6) : 3 e^{x} x^{2}

= 3 e^{x} x^{2}

What is the derivative of (3x^2-6x+6e^x) ?
The derivative of (3x^2-6x+6e^x) is 3e^xx^2
What is the first derivative of (3x^2-6x+6e^x) ?
The first derivative of (3x^2-6x+6e^x) is 3e^xx^2