en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= e^{x} x^{2}

Popular Examples

integral of e^ssin(1-s)

\int e^{s} sin (1 - s) d s

derivative of 5cos((pi/4 x)+pi/4)derivative of

5 cos ((\frac{π}{4} x) + \frac{π}{4})

derivative of sqrt(3x^2+y^2-1)

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

integral from 0 to 1 of (x-x^4)

\int_{0}^{1} (x - x^{4}) d x

area y=3x,y=7x^2 area

y = 3 x, y = 7 x^{2}

Frequently Asked Questions (FAQ)

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