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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{4 x ^{3} + 4 x + 4}{x ^{3} + x} d x

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integral of e^xx

\int e^{x} x d x

sum from n=1 to infinity of (n!)/(18^n)

n = 1 \sum \infty \frac{n !}{1 8 ^{n}}

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