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

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

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

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

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derivative of

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

7 e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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