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Popular >

derivative of e^x(11x^2-22x+22)

Solution

\frac{d}{d x} (e^{x} (11 x^{2} - 22 x + 22))

Solution

11 e^{x} x^{2}

Solution steps

\frac{d}{d x} (e^{x} (11 x^{2} - 22 x + 22))

Apply the Product Rule:

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

f = e^{x}, g = 11 x^{2} - 22 x + 22

= \frac{d}{d x} (e^{x}) (11 x^{2} - 22 x + 22) + \frac{d}{d x} (11 x^{2} - 22 x + 22) e^{x}

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

\frac{d}{d x} (11 x^{2} - 22 x + 22) = 22 x - 22

= e^{x} (11 x^{2} - 22 x + 22) + (22 x - 22) e^{x}

Simplify

e^{x} (11 x^{2} - 22 x + 22) + (22 x - 22) e^{x} : 11 e^{x} x^{2}

= 11 e^{x} x^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^x(11x^2-22x+22) ?
The derivative of e^x(11x^2-22x+22) is 11e^xx^2
What is the first derivative of e^x(11x^2-22x+22) ?
The first derivative of e^x(11x^2-22x+22) is 11e^xx^2