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

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

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

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

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derivative of

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

8 e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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