What is the derivative of e^x(8x^2-16x+16) ?

The derivative of e^x(8x^2-16x+16) is 8e^xx^2

What is the first derivative of e^x(8x^2-16x+16) ?

The first derivative of e^x(8x^2-16x+16) is 8e^xx^2

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\frac{d}{d x} (e^{x} (8 x^{2} - 16 x + 16))

8 e^{x} x^{2}

Solution steps

\frac{d}{d x} (e^{x} (8 x^{2} - 16 x + 16))

Apply the Product Rule:

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

f = e^{x}, g = 8 x^{2} - 16 x + 16

= \frac{d}{d x} (e^{x}) (8 x^{2} - 16 x + 16) + \frac{d}{d x} (8 x^{2} - 16 x + 16) e^{x}

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

\frac{d}{d x} (8 x^{2} - 16 x + 16) = 16 x - 16

= e^{x} (8 x^{2} - 16 x + 16) + (16 x - 16) e^{x}

Simplify

e^{x} (8 x^{2} - 16 x + 16) + (16 x - 16) e^{x} : 8 e^{x} x^{2}

= 8 e^{x} x^{2}

What is the derivative of e^x(8x^2-16x+16) ?
The derivative of e^x(8x^2-16x+16) is 8e^xx^2
What is the first derivative of e^x(8x^2-16x+16) ?
The first derivative of e^x(8x^2-16x+16) is 8e^xx^2