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Popular >

derivative of (4x^2-8x+8e^x)

Solution

\frac{d}{d x} ((4 x^{2} - 8 x + 8) e^{x})

Solution

4 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((4 x^{2} - 8 x + 8) e^{x})

Apply the Product Rule:

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

f = 4 x^{2} - 8 x + 8, g = e^{x}

= \frac{d}{d x} (4 x^{2} - 8 x + 8) e^{x} + \frac{d}{d x} (e^{x}) (4 x^{2} - 8 x + 8)

\frac{d}{d x} (4 x^{2} - 8 x + 8) = 8 x - 8

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

= (8 x - 8) e^{x} + e^{x} (4 x^{2} - 8 x + 8)

Simplify

(8 x - 8) e^{x} + e^{x} (4 x^{2} - 8 x + 8) : 4 e^{x} x^{2}

= 4 e^{x} x^{2}

Popular Examples

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\int \frac{1}{( x - 8 ) ( x ^{2} + 25 )} d x

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\int 2 x (x^{2} + 1)^{9} d x

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\frac{d}{d x} (- (x + 1) sin (\frac{x ^{2}}{2}))

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integral of 2cos(2x)-1

\int 2 cos (2 x) - 1 d x

Frequently Asked Questions (FAQ)

What is the derivative of (4x^2-8x+8e^x) ?
The derivative of (4x^2-8x+8e^x) is 4e^xx^2
What is the first derivative of (4x^2-8x+8e^x) ?
The first derivative of (4x^2-8x+8e^x) is 4e^xx^2