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^2-3x+1)

Solution

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

Solution

e^{x} x^{2} - e^{x} x - 2 e^{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x^{2} - 3 x + 1

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

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

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

= e^{x} (x^{2} - 3 x + 1) + (2 x - 3) e^{x}

Simplify

e^{x} (x^{2} - 3 x + 1) + (2 x - 3) e^{x} : e^{x} x^{2} - e^{x} x - 2 e^{x}

= e^{x} x^{2} - e^{x} x - 2 e^{x}

Popular Examples

integral of (x^2-2x)^3

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

tangent of f(t)= 8/(t^2),\at t=1 tangent of

f (t) = \frac{8}{t ^{2}}, at t = 1

derivative of (2x-7^{-1}(x+5))

\frac{d}{d x} ((2 x - 7)^{- 1} (x + 5))

derivative of y=(2x+3)/(5x-1)derivative of

y = \frac{2 x + 3}{5 x - 1}

derivative of y=-2(x+1)^2-4 derivative of

y = - 2 (x + 1)^{2} - 4

Frequently Asked Questions (FAQ)

What is the derivative of e^x(x^2-3x+1) ?
The derivative of e^x(x^2-3x+1) is e^xx^2-e^xx-2e^x
What is the first derivative of e^x(x^2-3x+1) ?
The first derivative of e^x(x^2-3x+1) is e^xx^2-e^xx-2e^x