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Popular >

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

Solution

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

Solution

4 e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of-4e^{-x}

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

integral from 1 to 2 of (10ln(x))/(x^2)

\int_{1}^{2} \frac{10 ln ( x )}{x ^{2}} d x

f(x)=arctan(5x)

f (x) = arctan (5 x)

integral from 1 to 2 of (x^2-3)

\int_{1}^{2} (x^{2} - 3) d x

integral of ((x-1))/(sqrt((x^2-4x+3)))

\int \frac{( x - 1 )}{( x ^{2} - 4 x + 3 )} d x

Frequently Asked Questions (FAQ)

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