What is the derivative of (7x^2-14x+14)e^x ?

The derivative of (7x^2-14x+14)e^x is 7e^xx^2

What is the first derivative of (7x^2-14x+14)e^x ?

The first derivative of (7x^2-14x+14)e^x is 7e^xx^2

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derivative of

(7 x^{2} - 14 x + 14) e^{x}

7 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((7 x^{2} - 14 x + 14) e^{x})

Apply the Product Rule:

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

f = 7 x^{2} - 14 x + 14, g = e^{x}

= \frac{d}{d x} (7 x^{2} - 14 x + 14) e^{x} + \frac{d}{d x} (e^{x}) (7 x^{2} - 14 x + 14)

\frac{d}{d x} (7 x^{2} - 14 x + 14) = 14 x - 14

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

= (14 x - 14) e^{x} + e^{x} (7 x^{2} - 14 x + 14)

Simplify

(14 x - 14) e^{x} + e^{x} (7 x^{2} - 14 x + 14) : 7 e^{x} x^{2}

= 7 e^{x} x^{2}

What is the derivative of (7x^2-14x+14)e^x ?
The derivative of (7x^2-14x+14)e^x is 7e^xx^2
What is the first derivative of (7x^2-14x+14)e^x ?
The first derivative of (7x^2-14x+14)e^x is 7e^xx^2