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Popular >

derivative of e^x(2x^2-4x+4)

Solution

\frac{d}{d x} (e^{x} (2 x^{2} - 4 x + 4))

Solution

2 e^{x} x^{2}

Solution steps

\frac{d}{d x} (e^{x} (2 x^{2} - 4 x + 4))

Apply the Product Rule:

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

f = e^{x}, g = 2 x^{2} - 4 x + 4

= \frac{d}{d x} (e^{x}) (2 x^{2} - 4 x + 4) + \frac{d}{d x} (2 x^{2} - 4 x + 4) e^{x}

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

\frac{d}{d x} (2 x^{2} - 4 x + 4) = 4 x - 4

= e^{x} (2 x^{2} - 4 x + 4) + (4 x - 4) e^{x}

Simplify

e^{x} (2 x^{2} - 4 x + 4) + (4 x - 4) e^{x} : 2 e^{x} x^{2}

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^x(2x^2-4x+4) ?
The derivative of e^x(2x^2-4x+4) is 2e^xx^2
What is the first derivative of e^x(2x^2-4x+4) ?
The first derivative of e^x(2x^2-4x+4) is 2e^xx^2