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Popular >

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

Solution

derivative of

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

Solution

2 e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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\frac{\partial}{\partial z} (e^{x} cos (y) + yz)

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n = 1 \sum \infty 2^{- 4 n}

Frequently Asked Questions (FAQ)

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