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Popular >

derivative of (7x^2-14x+14e^x)

Solution

\frac{d}{d x} ((7 x^{2} - 14 x + 14) e^{x})

Solution

7 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((7 x^{2} - 14 x + 14) e^{x})

Apply the Product Rule:

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

f = 7 x^{2} - 14 x + 14, g = e^{x}

= \frac{d}{d x} (7 x^{2} - 14 x + 14) e^{x} + \frac{d}{d x} (e^{x}) (7 x^{2} - 14 x + 14)

\frac{d}{d x} (7 x^{2} - 14 x + 14) = 14 x - 14

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

= (14 x - 14) e^{x} + e^{x} (7 x^{2} - 14 x + 14)

Simplify

(14 x - 14) e^{x} + e^{x} (7 x^{2} - 14 x + 14) : 7 e^{x} x^{2}

= 7 e^{x} x^{2}

Popular Examples

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

derivative of-(30/(x^4))

\frac{d}{d x} (- \frac{30}{x ^{4}})

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

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\int \frac{ln ( 4 x ^{2} )}{x} d x

integral of xe^{-x/(100)}

\int x e^{- \frac{x}{100}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (7x^2-14x+14e^x) ?
The derivative of (7x^2-14x+14e^x) is 7e^xx^2
What is the first derivative of (7x^2-14x+14e^x) ?
The first derivative of (7x^2-14x+14e^x) is 7e^xx^2